d change of distance s = step 1: variables step 3:...

Name: _____________________

Period: _____________________

cstephenmurray.com Copyright © 2008, C. Stephen Murray Legal copying of this worksheet requires written permission.

Unit 6:1

Speed

Speed

Speed is how fast something is moving. Precisely, it is how far an object travels in a certain amount

of time. The standard metric units are meters per second (m/s), but any units of distance divided by

time will work (like miles per hour [mph] or cm per sec [cps], etc).

S =

Speed equal change of distance (distanced traveled)

divided by change of time.

Change of Distance (in meters)

Change of Time (in seconds)

Speed (in meter/sec)

∆D

∆T

Where ∆D = Dfinal − Dinitial

Ex. A plane flies 200 meters in 5 sec. Calculate its speed.

Step 1: Variables S = ________

∆D = 200 m

∆T = 5 sec

Step 2: Formula

Step 3: Put in numbers and solve

Step 4: Check units

S = 40 m/sec D

ST

∆=

∆

200

5

40

DS

T

S

∆= =

∆

=

Speed is proportional to distance:

A faster object goes farther, in the same amount of time.

Speed is indirectly proportional to time:

A faster object travels the same distance in less time.

Each dot represents an object’s position at regular time intervals (time is constant).

Measuring Speed Initial Position Final Position 25 m

Distance Traveled

0:05.0 Elapsed Time

5 sec 0:00.0

To measure speed you must measure

the distance traveled and the elapsed

time.

Measure distance in meters using a

meter stick or measuring tape.

Measure time with a stopwatch or

with photogates.

Photogates (which start and stop when

an object breaks beams of light) are a

very accurate and precise method of

measuring time.

2 5 m5 m /s

5 sec

DS

T

∆= = =

∆

100m in 10sec

200m in 10sec

1

10010m/s

10

DS

T

∆= = =

∆

2

20020m/s

10

DS

T

∆= = =

∆

Doubling the distance,

doubles the speed.

200m in 20sec

200m in 10sec 2

20020m/s

10

DS

T

∆= = =

∆

1

20010m/s

20

DS

T

∆= = =

∆

Doubling the time,

halves the speed.

Constant Speed

A slower object can travel the same distance as a faster object, it

just takes more time. A fast object travels the same distance faster.

If an object moves at constant speed,

it travels the same amount of distance

each second. Notice that there is

equal space between each dot.

Why we use change of distance:

A tree 4 m away

for 2 sec has a

speed of zero

— it hasn’t moved.

That’s why we

have to use ∆D

(change of distance) instead of

distance (D).

An object has to be moving to

have speed.

Physics Explains Mathematics: If ∆T = 0 (in S = ∆D/∆T), then an

object is in two places at once,

which is impossible. This is why

dividing by zero is undefined: it

makes no physical sense!

Fast object

Slow object

Name: _____________________

Period: _____________________


Unit 6:1

1. Speed

2. Distance Traveled

3. Elapsed Time

4. ∆

5. Constant Speed

A. How far an object moves between two positions.

B. When an object covers equal amounts of time each second.

C. The rate of how fast an object travels a particular distance.

D. How many seconds it takes for an event to occur.

E. Delta: means “change of”.

True or false (and why): “A fast car goes farther.”

Can a slow object travel as far as a fast object?

Explain.

Why do we have to use change of distance (∆D) instead of just

distance (D)?

A bike moves 50 m in 10 seconds.

Calculate the speed of the bike.

Step 1: Variables:

S =

∆D =

∆T =

Step 2: Formula:

Step 3: Plug in numbers and solve:

Step 4: Give answer with units:

1. Slow speed

2. Fast speed

3. Photogate

4. Directly Proportional

5. Indirectly Proportional

A. An object that travels a long distance quickly.

B. Can travel a long distance, but requires a lot of time.

C. Uses a beam of light to start and stop a timer.

D. One quantity increases as another quantity increases.

E. One quantity decreases as another quantity increases.

_____ 5 mm/sec

_____ 10 inches

_____ 50 m/s2

____ 20 meters/sec

____ 228 meters

____ 8 minutes

____ 15 ft/min

____ 78 sec

____ 6 Newtons

Mark these as Speed, Distance, Time, or Other

A car travels 60 m/s for 10 secs.

Calculate how far it traveled.

Step 1: __________

Step 2: __________

Step 3: ______________________

Step 4: ______________________

On holiday, a family travels from Meyerville (10 miles away)

to Sprytown (70 miles away), in 3 hours. Find their speed.

Step 1: __________

Step 2: __________

Step 3: ______________________

Step 4: ______________________

A car travels 200 miles in 4 hours.

Calculate the car’s speed.

Step 1: Variables:

S =

∆D =

∆T =

Step 2: Formula:

Step 3: Plug in numbers and solve:

Step 4: Give answer with units:

____ Distance is constant and time increases.

____ Time is constant and distance decreases.

____ Time is constant and distance increases.

____ Distance is constant and time decreases.

Will Speed Increase or Decrease?

1. Is the above motion at constant speed?

2. Why or why not?

3. Each dot = 1 sec. How long did it take to go 15 m?

4. Calculate the object’s speed.

5. How would the dots change if it were moving faster?

start

Name: _____________________

Period: _____________________


Name: _____________________

Period: _____________________


Unit 6:2

Velocity and Acceleration

Example: A person

walks 4 m/s—speed (no direction).

Speed vs. Velocity Velocity is speed with direction.

20 m/s

north

20 m/s

west Same speed; different

velocities because they

have different directions.

Scalars vs. Vectors

Remember: Speed is a Scalar; Velocity is a Vector.

Vectors require direction;

Scalars only need magnitude (how big).

Vectors require magnitude (how much) and direction, often

vectors can cancel each other out (not acceleration, though).

12 m/s west Magnitude Direction

Speed: 12 m/s.

Velocity: 12 m/s west. Velocity changes when direction changes.

Ex. A plane starts at rest and ends up going

200 m/s in 10 secs. Calculate its acceleration.

Step 1: Variables Vi = 0 m/s (at rest)

Vf = 200 m/s

T = 10 sec

a = _________

Step 2: Formula

V

aT

∆=

∆


Step 4: Add units

a = 20 m/s2

200 0

10

20020

10

f iV VVa

T T

a

−∆ −= = =

∆ ∆

= =

Acceleration

Acceleration is how fast

you change velocity OR

how much the velocity

changed in a certain

amount of time.

An object accelerates

when it changes speed

OR changes direction!

a =

Acceleration equal change of velocity

divided by change of time.

Change of Velocity (in meters/sec)

Change of Time (in seconds)

Acceleration

(in m/s2)

∆V

∆T

, so, final initial

final initial

V VV V V a

T

−∆ = − =

∆

Ex. A race car starts at 40 m/s slows to 10 m/s

in 5 seconds. Calculate the car’s acceleration.

Step 1: Variables Vi = 40 m/s

Vf = 10 m/s

T = 5 sec

a = _________

Step 2: Formula

V

aT

∆=

∆


Step 4: Add units

a = –6 m/s2

10 40

5

306

5

f iV VVa

T T

a

−∆ −= = =

∆ ∆

−= = −

Neg. means

slowing

down

Negative

acceleration

means an object

is slowing down

OR speeding up

in the negative

direction.

Slowing down

is also called

“deceleration”.

Finding ∆V.

∆ always = final – initial.

∆V = Vfinal – Vinitial OR

Final velocity – Initial velocity.

If ∆V is positive the object is

speeding up.

If ∆V is negative the object is

slowing down (see below).

Distance and Acceleration

Pos. means

speeding

up

Measuring Acceleration

To measure an object’s

acceleration you need to

measure the object’s

velocity before and after

the acceleration.

If the object starts at rest

you know that Vi = 0m/s.

If the object stops

you know that Vf = 0m/s.

Points are equal distance, so velocity is constant.

Since the velocity is constant, the initial and final velocity

are equal and the acceleration equals zero.

The distance between the points is increasing, so velocity

is increasing. The object is accelerating: traveling faster

each second and covering more distance every second.

An object that is accelerating will travel farther each second.

4 m

1 sec

4 m /s

i

in it ia l

DV

T

V

∆= =

∆

=

8 m

1 se c

8 m /s

f

fin a l

DV

T

V

∆= =

∆

=

2

8 4

2

42m/s

2

f i

initial

V Va

T

V

− −= =

∆

= =

Constant Speed—Equal Distance Positive Acceleration—Increasing Distance

Accelerates

for 2 seconds

So ∆T = 2 sec 4 m in 1 sec

Measure Vf

(Final Velocity)

8 m in 1 sec

Measure Vi

(Initial Velocity)

Measure ∆T

(Time it took to Accelerate)

Name: _____________________

Period: _____________________


Unit 6:2

Mass, Time, Distance, Velocity, or Acceleration?

___ 2 hrs

___ 3 m/s

___ 6 mph/sec

____5 sec

____9 mph

____12 m

____8 kg

____4 m/s2

____1 in

___A bike goes 25 m/s toward

main street.

___A person walks 4 mph.

___A plane flies 200 m/s.

___A bird flies 100 mph due

south.

Speed (S) or Velocity (V)

___ 40 mph toward Dallas.

___ 3 m/s2 to the left.

___ 10 meters up the hill.

___ 12 meter per sec2.

___ Direction matters.

___ No direction is needed

Scalar (S) or Vector (V)

A dragster’s top acceleration is 60 m/s2. If it starts from rest at the

starting line, how fast will it be going after 3 seconds?

Variables:

Formula:

Solve:

A person starts running from 2 m/s to 6 m/s in 2 seconds.

Calculate the person’s acceleration.

Variables:

Formula:

Solve:

A car travels 30 m in 5 seconds. After accelerating for 3 seconds,

it travels 20 m in 2 seconds. Calculate the car’s acceleration.

1) Find Vi.

2) Find Vf.

3) Calculate a.

A plane stops from 250 mph in 25 seconds.

Calculate the planes acceleration.

Variables:

Formula:

Solve:

10 m/s

10 m/s

Accelerating? Yes, No, or Maybe?

___ At constant velocity.

___ Going 5 m/s then going 3 m/s.

___ A car going around a corner.

(see graphic at right).

___ At constant speed.

___ Stopping.

___ A car at rest.

Object A accelerates at 10 m/s2; Object B accelerates at 5 m/s2.

___ Which one will go faster?

___ Which one will take more time to reach a high speed?

___ If they start at rest, which one will reach 40 m/s first?

___ Which one goes farther (longer distance)?

___ Which one will be 100m away sooner?

Object A

Object B

Object C

Choose which of the above applies to the following

____ Constant speed.

____ Positive acceleration.

____ At constant velocity.

____ Accelerating.

____ Decelerating.

____ Acceleration = 0.

____ Distance increases

____ Starts at rest.

____ Is stopping.

____ Constant direction.

____ Negative acceleration.

____ Vi = Vf

Object D

Give what you know for the following: (Vi, Vf, or a)

An object at constant velocity.

An object that is stopping.

An object that accelerates from rest.

An object at rest.

Name: _____________________

Period: _____________________


Name: _____________________

Period: _____________________


Unit 6:3

Graphing Linear Motion

Conventions: X-axis (horizontal): Independent or manipulated variable.

Y-axis (vertical): Dependent or responsive variable.

Meaning of Slope Changes The slope of a position vs. time graph is speed. The slope of a velocity vs. time graph

is acceleration. Yet for some graph, the slope has no physical meaning.

Position vs. Time

Graphs

Graphing Variables

A Position vs. Time graph shows where an object is at a particular time. The slope of a position vs. time

graph shows the speed of an object. A steeper line shows faster speed. A downward line means negative

speed (moving left or coming back).

A steeper line = a faster speed.

306m/s

5LineA

DS

T

∆= = =

∆

303m/s

10LineB

DS

T

∆= = =

∆

Object B travels 30 m in 10 seconds.

Line B shows slow positive speed.

Position vs. Time

0

5

10

15

20

25

30

35

0 1 2 3 4 5 6 7 8 9 10 11 12

Time (sec)

Po

sit

ion

(m

)

Line A fa

st spe

ed

slow sp

eed Line B

negative speed Line D

Starting position (t = 0)

no speed Line C

Object C stays 15 m away.

Line C shows a speed of zero.

00m/s

10LineC

DS

T

∆= = =

∆

Object D travels –20 m in 10 seconds.

Line D shows slow negative speed.

202m/s

10LineD

DS

T

∆ −= = = −

∆

Object A travels 30 m in 5 seconds.

Line A shows fast positive speed.

To figure out what the

slope of a graph means:

divide the y-axis units by

the x-axis units to find the

units for the slope.

Scientists have rules for choosing which variable is graphed on which axis. This allows scientists to

understand how an experiment was conducted just by reading the graph.

Independent

vs. Dependent The independent vari-

able is not affected by

the changing depend-

ent variable. The de-

pendent variable

changes as the inde-

pendent variable

Manipulated

vs. Responsive Sometimes it is hard to

determine which is the

independent variable. In

these cases, the variable

that you are manipulating

(varying) will graphed on

the x-axis.

Velocity vs. Time

Dep

end

ent

vari

ab

le

Vel

oci

ty (

in m

/s)

Time (in sec)

Independent variable

Acceleration vs. Force

Res

po

nsi

ve v

ari

ab

le

Acce

lera

tio

n (

in m

/s2)

Force (in N)

Manipulated variable

The above object’s acceleration

changes (responds) as the force is

changed (manipulated).

This graph shows the change of acceleration

over time which is undefined.

Acceleration vs. Time

Acce

lera

tio

n

(in

m/s

2)

Time (in sec)

23m/s

m/s ?s

rise ySlope

run x

∆= = = = =

∆

Velocity vs. Time

Vel

oci

ty (

in m

/s)

Time (in sec)

This graph shows the change of velocity

over time which is acceleration.

2m/sm/s acceleration

s

rise ySlope

run x

∆= = = = =

∆

Slope = −acceleration

Time (as in “a particular

moment in time”) is always an

independent variable (x-axis)

because nothing stops time.

Time does not change with

speed; speed changes over time.

Duration (how long it takes) can be

dependent (y-axis). Ex. The period

of a spring (how long it takes to

move back and forth) changes as

more mass is added. Mass is inde-

pendent, not period of time.

The slope of

this graph

means nothing.

The manipulated variable is the

one you are changing in your ex-

periment and is often the experi-

mental variable.

Meaning of Slope

units of y-axis

units of x-axis

rise

run=

=

Name: _____________________

Period: _____________________


Unit 6:3

When was the object moving at 150 m/s? ______________________

How fast is the object going after 10 seconds? __________________

What was the initial velocity of the object? _____________________

How much speed does it gain in the first 5 seconds? ______________

Find the slope of the graph (must show work) ___________________

What does the slope you just found stand for? __________________

1. Linear

2. Responsive variable

3. Independent variable

4. Dependent variable

5. Slope

6. Manipulated variable

A. Vertical axis (y) variable.

B. The variable you change.

C. Any straight line graph.

D. Measure of how steep a line is.

E. The variable on the horizontal axis (x-axis).

F. What changes because you change something.

Position vs. Time

0

20

40

60

80

100

120

0 2 4 6 8 10 12

Time (sec)

Po

sit

ion

(m

)

What does the slope of this line show? ________________________

How much time does it take Object A to travel 100m? ___________

How much time does it take Object B to travel 100m? ___________

Which Object (A or B) has the faster velocity? _________________

Object C starts where? ________ Object C ends where? _________

Which line shows negative speed? ___________________________

Which line shows positive speed? ___________________________

Which line shows an object at rest? __________________________

What is Object D’s initial position? __________________________

Which is the independent variable? ___________________________

Which is the dependent variable? _____________________________

Where was the object at 4 seconds? ___________________________

Where did the object begin? _________________________________

Find the slope of the graph (must show work)

What does the slope you just found stand for? ___________________

The slope of this graph means:

Which segment shows:

Increasing velocity:

Constant velocity:

Positive acceleration:

Negative acceleration:

Speeding up:

Slowing down:

Position vs. Time

Time

Po

siti

on A

B C D

Which segments shows:

At rest:

Fast speed:

Slow speed:

Going backwards:

Going forward:

Negative speed:

Speed equals zero:

Position vs. Time

0

2

4

6

8

10

12

14

16

18

0 1 2 3 4 5 6

Time (sec)

Po

siti

on (

m)

Velocity vs. Time

Time

Vel

oci

ty

A B

C D

Circle the Independent Variable

A. Time or Acceleration

B. Velocity or Time

C. Time or Position

Circle the Manipulated Variable for these Graphs

A. Force on an object or Acceleration of the object?

B. Period of a Spring or Mass hung from the spring?

C. Number of batteries or Brightness of a bulb?

Velocity vs. Time

0

50

100

150

200

250

300

350

0 1 2 3 4 5 6 7 8 9 10 11

Time (secs)

Ve

loc

ity

(m

/s)

A B

C

D

Name: _____________________

Period: _____________________


Name: _____________________

Period: _____________________


Unit 6:4 Momentum and Conservation of Momentum

Momentum

A house has no momentum because it is not moving (v = 0 m/s).

A slow bowling ball has little momentum:

a lot of mass, but low velocity.

A fast baseball has a lot of momentum: small mass, but high velocity.

Ex. A 40 kg boy on a

skateboard throws a

1 kg ball 20 m/s to the

left. If both were at

rest beforehand, find

how fast the boy is

going afterward.

Ex. How much momentum does a 30 kg object going 4 m/s have?

Variables: m = 30 kg v = 4 m/s p = _____

Solve:

p = mv = (30kg)(4m/s)

= 120 kgm/s

p = mv

Mass (in kg)

Velocity (in m/sec)

Momentum

(in kgm/sec)

Momentum equals mass times velocity.

Momentum is how hard it is to stop a moving object. Momentum depends on

both mass and velocity. An object gains momentum as it gains velocity. A heavy object will have more mo-mentum than a light object,

if at the same velocity.

Momentum is a Vector

As a vector, direction matters. So, momentum can be positive or

negative and can be added or subtracted.

Negative momentum

20 kg 10 m/s

200 kgm/s

20 kg -10 m/s

-200 kgm/s

Positive momentum

Net Momentum To find the net momentum, add up all of the individual momentums. Net momentum can add up to zero, if the objects are moving different directions.

pnet = Σp

Σp = p1 + p2 + …

Net Momentum

Sum of all Momentum

Add up all of the momentums

p1 = 50 kgm/s

10 kg 5 m/s

10 kg -5 m/s

p2 = -50 kgm/s

pnet = Σp = p1 + p2 =

50 + -50 = 0 kgm/s

Ex. Calculate the net momentum of the two objects.

Law of Conservation of Momentum:

If there are no outside forces, momentum is always conserved OR Σpbefore = Σpafter.

Momentum is Conserved In any interaction (when objects collide or push off from each other) momentum is conserved,

meaning that the net momentum before (Σpbefore) equals the net momentum after (Σpafter).

ball = 1 kg

vL = -20 m/s

skater = 40 kg vR = ?

Momentum is conserved:

Σpbefore = Σpafter

0 = 1(-20) + 40(v)

0 = -20 + 40v

20 = 40v

v = 0.5m/s

(to the right)

Momentum Can Be Transferred When two objects collide momentum is transferred from one object to the other.

M1

fast

M2

slow

Before collision

M2

fast

M1

slow

After collision

M2 speeds up after the collision because it gained momentum from M1.

Momentum is transferred in collisions.

The ball on the left transfers its momentum

thru the three middle balls to the ball on the right.

After Before

Momentum

is conserved: Σpbefore = Σpafter

0 = procket – pfuel

procket = pfuel

the fuel

goes down.

The rocket

goes up because

Conservation of momentum is how rockets move. Gases are expelled

at a very fast velocity, pushing the rocket in the opposite direction.

Thrown, Shot or Launched Objects: Thrown objects are initially rest, so v = 0 and Σpbefore = 0.

Afterwards, Σpafter must still = 0. How? Only if the momentums of

the two objects are equal and opposite: pLeft = pRight and pR – pL = 0.

2 kg

4 m/s

5 kg

6 m/s

BEFORE

2 kg

v = ?

5 kg

2 m/s

AFTER

? ?

p1b = 2(4) p2b = 5(-6) p1a = 3(v) p2a = 5(-2)

Σpbefore = Σpafter

p1b + p2b = p1a + p2a

2(4) + 5(-6) = 2v + 5(-2)

8 – 30 = 2v + 5(-2)

-22 = 2v – 10

-12 = 2v

v = -6 m/s

The negative means the object

ends up going to the left.

Keep directions straight! (left is negative)

Collisions When objects collide, momentum is transferred,

but the total momentum does not change.

The Law of Conservation of Momentum can

tell us unknown velocities and directions.

“b” means “before”

“a” means “after”

Name: _____________________

Period: _____________________


Unit 6:4

Find the momentum of a 25 kg object going 4 m/s to the right.

_______________________________________________

A 3 kg object is going 22 m/s to the left. Find its momentum.

________________________________________________

A ball has 2 kgm/s of momentum when thrown 8 m/s to the right.

Find the mass of the ball.

_______________________________________________

A 25 kg cart has -125 kgm/s of momentum. How fast is the

cart going?

_______________________________________________

Two objects are at rest. Find the net momentum of the two.

_____________________________________________

A 50 kg girl on ice skates throws a 5 kg ball to the left. If the ball

ends up going 20 m/s, .

A) If the girl and ball are initially at rest, what was their

velocities? v1i = v2i =

B) What is the net momentum of the girl and ball before

Σpbefore =

B) How much momentum do the girl and ball have to have

afterwards? Σpafter =

C) Use the Law of Conservation of Momentum to find how fast

the girl is going afterwards.

1. Momentum

2. kgm/sec

3. Law of Conserva-

tion of Momentum

4. Net momentum

5. Σp

A. The total momentum will stay the same when objects interact.

B. Units for momentum.

C. Product of an object’s mass and velocity.

D. Means to add together all of the individual momentums (p1 + p2 …).

E. The total of all the momentums.

A bullet

A fast car

A slow

baseball

A house

A fast train

Number these from least (1) to most (5) momentum.

6 kg 5 m/s

8 kg 2 m/s

How is it possible that two objects have a net momentum equal

to zero? (There are two ways.)

How can an object have negative momentum?

If a fast object hits a slower object, why does the slower object

speed up?

If two objects have 24 kgm/s of momentum before they collide.

How much momentum do the two objects have afterwards?

How does a rocket fly in space if it has nothing to push on?

Calculate the momentum of the 100 kg car.

Constant Speed

3.0 0.0

Calculate the net momentum

of these two objects.

If the tapetimer above shows the position of an object every

second, how does the momentum of the object change?

Position vs. Time

0

3

6

9

12

15

0 1 2 3 4 5 6 7

Time (sec)

Po

sit

ion

(m

)

If the object has

6 kg of mass, find

its momentum

from the graph.

Name: _____________________

Period: _____________________


Name: _____________________

Period: _____________________


Unit 6:5

Linear Motion Review

mv = m times v

F/a = F _______ a

T2 + T1 = T2 _______ T1

mv = m _______ v

∆D/∆T = ∆D _______ ∆T

Match the variables with the quantities.

1. a = _____________

2. S or v = _____________

3. D = _____________

4. F = _____________

5. T = _____________

sec

m/sec

43 m/s2

45 meters

22 newtons

Equation: S = ∆D/∆T;

solve for ∆D.

If ∆v = v2 – v1,

solve for v2:

If p = mv, solve for m.

If a = ∆V/∆T,

solve for ∆T:

For the following problems, show all work and steps. A plane stops from 300 mph in 15 seconds. Calculate the planes acceleration. A bike going 3 m/s ends up going 9 m/s after 2 seconds.

Calculate the bike’s acceleration.

A car travels 35 m in 5 secs. Calculate its speed.

Variables:

Formula:

Solution:

A bike goes 12 m/s for 6 seconds.

Calculate how far the bike traveled.

Variables:

Formula:

Solution:

A

B

C

D

E Choose which of the above

object’s motion applies to the

following (can be more than one):

______Vi = 0

______Decelerating

______Constant speed

______Is stopping

______Positive acceleration

______At constant velocity

______Vf = 0

_____ Accelerating

_____ Acceleration = 0

_____ Distance is increasing

_____ Starts at rest

_____ Constant direction

_____ Negative acceleration

_____ Vi = Vf

For object B above:

A) If there is 1 second between each dot, when did the object

reach 12 m?

B) Find the speed of object B.

What do you need to know in order to find an object’s speed?

What does ∆ mean (and give the formula)?

Which has the faster speed? Car A or Car B?

Both go the same distance, but Car B gets there sooner.

In the same amount of time, Car A goes farther.

TA = TB, but DA < DB.

Car 1 is going 20 m/s. Car 2 is going 30 m/s.

Which one travels 100 m first?

Which one can travel a greater distance?

Which one travels farther in more time?

An object has a velocity of 5 m/s and starts 0 m away from you.

A) How far does it travel each second?

B) Where is it after 1 second?

C) Where is it after 2 seconds?

D) Where is it after 5 seconds?

E) How far does it travel between seconds 7 and 8?

Speed (S) or Velocity (V)

____ A car travels 10 m/s left.

____ A bird flies 20 m/s.

____ A bike goes 10 m/s toward town.

____ 10 m/s.

____ 60 mph toward Austin.

____ Direction matters.

Scalar (S) or Vector (V)

Name: _____________________

Period: _____________________


Unit 6:5

Position vs. Time

Time

Po

siti

on

Which graph segments fit

the following:

At rest:

Fast speed:

Slow speed:

Going backwards:

Going forward:

Speed vs. Time

Time

Sp

eed

Which graph segments

fit the following:

Constant speed:

Negative acceleration:

Positive Acceleration:

Slowing down:

Acceleration = 0:

For the following problems, show all work and steps. A 4 kg object is moving 6 m/s to the left. Calculate momentum. A 10 kg object has 58 kgm/s of momentum. Find its velocity. Find the net momentum of the two objects at the right.

Which is the independent variable? __________________________

Which is the dependent variable?_____________________________

Where was the object at 4 seconds? __________________________

Where did the object start? _________________________________

When did the object reach 8 meters? __________________________

Find the slope of the graph (show work)

What does the slope you just found stand for? __________________

Position vs. Time

02468

101214161820

0 1 2 3 4 5 6

Time (sec)

Line A

An object accelerates at 10 m/s2. Answer the following:

A) If it starts at rest, how fast is it going after 1 second?

B) After 2 seconds, how fast is it going?

C) If it starts at 5 m/s, how fast would it be going after 1 second?

Fast car

Fast

truck

Fast plane

Fast

hammer

A

mountain

Number these from most (1) to least (5) momentum.

If two objects have a net momentum of 45 kgm/s before they

collide, how much momentum will they have after they collide?

An astronaut is by herself in space. All she has is a box of tools.

How can she get to her ship that is to her left?

How is it possible that two moving objects can collide and stop

moving?

A 200 kg cannon shoots a 2 kg cannonball. If the ball ends up

going 300 m/s to the right:

A) If they are both at rest beforehand, what is Σpbefore?

B) What is Σpafter?

C) Is the ball’s final p positive or negative (pball A)?

D) Is the cannon’s final p positive or negative (pcannon A)?

E) Find the velocity of the cannon afterwards vcannon A)?

10 kg

4 m/s

8 kg

3 m/s

Po

siti

on (

m)

A

B

C

D

D

C

A

B

Name: _____________________

Period: _____________________


Name: _____________________

Period: _____________________


Unit 6:S1

Variable Units Variable Name

d m (meters) distance

v m/s velocity

t sec time

a m/s2 acceleration

F N (newtons) force

m kg mass

p kgm/s momentum

W J (joules) work

How to Solve Word Problems

Variable Units Variable Name

d m (meters) distance

v m/s velocity

t sec time

a m/s2 acceleration

F N (newtons) force

m kg mass

p kgm/s momentum

W J (joules) work

Variable Sheet Step 1: Use the Variable Sheet to Assign Variables

The units tell you what variable to use.

Problem: A spring pulls with 30 N on a 6 kg metal cart.

Find the acceleration that occurs.

F = 30 N

m = 6 kg

a = ____

Always assign variables here!

This is your unknown. It MUST

be included in your variables!

Equation Sheet

Equations

dv

t=

f iv v

at

−=

p mv=

W Fd=

F ma=

WP

t=

PE mgh=

21

2KE mv=

Equations

Step 2: Use the Equation Sheet to Select a Formula. Find an equation that contains all the variables in

your variable list INCLUDING your unknown.



F = 30 N

m = 6 kg

a = ____

F ma=ALWAYS put your formula

here: WITHOUT NUMBERS!

Sometimes it is easier

to solve for the unknown

BEFORE putting

in the numbers.

Step 3: Put in the Numbers and Do the Math. (See “Algebra Help”, if you need help with the math.)



F = 30 N

m = 6 kg

a = ____ 30 6

F ma

a

=

=

30 6

6 6

5

a

a

=

=

Step 4: Make Sure the Answer Has the Correct Units. In science, the answer is not completely correct without units.



F = 30 N

m = 6 kg

a = 5 m/s2 30 6

F ma

a

=

=2

30 6

6 6

5 /

a

a m s

=

=

Variable Sheet

The chart shows

that acceleration has

the units of m/s2.

Put your answer back in your variable

list, where it will be easy to find if you

need it for another problem or step.

Make sure your variables are in

STANDARD UNITS (convert centimeters

to meters, for instance). Most equations

will only work with standard units!

Big Hint

Name: _____________________

Period: _____________________


Unit 6:S1

How To Do the Algebra

Notation Addition and subtraction are notated the same in physics equations

as in basic mathematics, but not so for multiplication or division.

dv d t

t= = ÷ F ma m x a= =

Two letters or

numbers next to

each other show

multiplication.

A letter below

another letter

means division.

Do Not Keep Units Use units to assign variables and to be sure you are using standard units (meters

instead of centimeters, for instance), then put in just the numbers—no units! Make

sure, though, to put the units back on the answer at the end.

(25)(10)(5)PE =

Still correct, but less confusing 2(25kg)(10m/s )(5m)PE =

Correct, but confusing

Equations are Equal The equal sign means that both sides are equal. Therefore, anything done

to one side must be done to the other or the equation is no longer equal.

35 10

35 10 10

f

f

v

v

= −

= − +

Equal

Not Equal

35 10

35 10 10 10

f

f

v

v

= −

+ = − +

Equal

Still Equal

The Algebra

Division Moves Multiplication Multiplication Moves Division

Subtraction Moves Addition Addition Moves Subtraction

F ma

F ma

m m

Fa

m

=

=

=

Variables Numbers

2

35 7

35 7

7 7

5m/s

a

a

a

=

=

=

Variables Numbers

123

12(3) 33

36 J

W

W

W

=

=

=

WP

t

WPt t

t

Pt W

=

=

=

f i

i f i i

i f

V V V

V V V V V

V V V

∆ = −

∆ + = − +

∆ + =

Variables Numbers

1 2

2 1 2 2

2 1

net

net

net

F F F

F F F F F

F F F

= +

− = + −

− =

Variables Numbers

1

1

1

15 6

15 6 6 6

9N

F

F

F

= +

− = + −

=

24 8

24 8 8 8

32m/s

f

f

f

V

V

V

= −

+ = − +

=

The following shows only the four most common algebraic operations.

There are many more. They will be presented to you as necessary.

Order Matters! “Please Excuse My Dear Aunt Sally” will help you remember you order of

operations: Parenthesis; Exponents; Multiply; Divide; Add; Subtract.

Correct

2(4 2) 3 2(2) 3 4 3 7− + = + = + =

Incorrect

2(4 2) 3 2(2) 3 2(5) 10− + = + = =

Name: _____________________

Period: _____________________


Unit 6:S2 Practice with Word Problems

A car starts at rest. After 4 seconds it is going 24 m/s.

What was the car’s acceleration?

Variables:

Equation:

Solve:

A bike moves 30 m in 5 seconds.

Calculate the speed of the bike.

Variables:

Equation:

Solve:

A 12 N force pushes on a 3 kg object.

Find the object’s acceleration.

Variables:

Equation:

Solve:

A 10 N force pushes for 3 m.

How much work was done on the object?

Variables:

Equation:

Solve:

Using the same procedure as above,

solve the following word problems.

A bike goes 10 m/s for 20 seconds. Calculate how far the bike

traveled.

A 2 kg object is moving 12 m/s. How much momentum does

the object have?

If a person pushes with 3 N and does 18 J of work. How far did

they push the object?

Challenge problems:

A person walks 240 meters at 3 m/s. How long did it take?

Grandma lives 120 miles away. Dinner is at 5 p.m. The speed

limit is 60 mph. What time do you need to leave to be on time?

How fast is Nigel moving, if he is at constant speed?

0:00.0 0:04.0

Constant Speed

Position vs. Time

0

5

10

15

20

25

30

35

40

45

50

0 2 4 6 8 10 12 14 16 18 20

Time (sec)

Po

sit

ion

(m

)

Find the slope of the graph (including units).

Name: _____________________

Period: _____________________


Name: _____________________

Period: _____________________


Physics Variables and Units

Variable Units Variable Name Notes:

Name: _____________________

Period: _____________________


We follow safety procedures not for the expected, but for the unexpected.

(If we knew something would happen, we could plan for it.)

1. Carefully follow all instructions given by your teacher (the most important safety feature in any classroom).

Physics Safety

2. Wear eye protection when

A. objects are launched (projectiles) or thrown.

B. objects are under stress. Materials can break and send shards or splinters flying. A broken

meter stick could easily send a splinter into your eye.

C. Whenever there is glass: beakers; graduated cylinders; light bulbs . Broken glass can fly a

very long way (several meters), so pieces of glass can certainly get to your eye.

Wear goggles whenever you move any glass, even if containers are empty.

3. Do NOT wear loose clothing, loose long hair, or dangling jewelry when

A. working near moving objects or motors. They could get caught in a motor or a lever and

pull you in.

B. working near an open flame. Even if not flammable, fabrics can melt to your skin caus

ing severe burns. Hair burns very quickly. Long or loose sleeves must be buttoned at the

wrist, securely rolled up, or taped. Hair must be pulled back.

4. Wear closed-toed shoes during ALL labs. Not only can sharp or heavy objects do obvious

damage, but even a 1 kilogram mass dropped from a lab table could break a toe.

5. Know the location of the following class safety equipment.

A. Fire extinguisher

B. Fire blanket.

C. First Aid Kit.

D. MSDS sheets (Material Safety Data Sheet).

E. Alternate Fire Exit.

F. Eye wash station

6. Never perform unauthorized experiments ESPECIALLY with chemicals.

A. Many chemical combinations can produce hazardous and deadly reactions, which

could even be odorless. “Let’s see what happens” are famous last words.

B. Even seemingly innocent experiments can be dangerous. Ice bombs can produce

unpredictable and deadly explosions. Even ice in melted wax can erupt to

produce a shower of burning steam or cause the glass beaker to fall and break.

7. Follow basic chemistry safety when working with chemicals.

A. Waft when smelling something (wave some of the smell towards you).

B. Wear apron, goggles, and maybe even gloves.

C. When heating liquids

i. use an open containers to allow built up pressure to be released;

ii. do not lean over or look into the glassware;

iii. point the opening away from others, in case it erupts;

D. Keep chemicals and glass away from the edge of the lab table.

E. Never sample or taste anything in the lab unless instructed by your teacher. Clean

glassware could have residue from past chemicals. Edible products might absorb

chemicals from the air. Don’t take the risk!

F. Tell your teacher if glass becomes broken. Using the dust pan and brush dispose of the

broken glass in the glass breakage box.

8. Use your brain. Pay attention. Don’t goof off! “It’s all fun and games until someone gets hurt.” You’ve heard this before and it the lab it could

very easily come true. Resist the urge to play in the lab. Think first to stay safe.

CONSIDER ALL UNKNOWNS POTENTIALLY DANGEROUS UNTIL PROVEN OTHERWISE!

Name: _____________________

Period: _____________________


Curriculum Notes from Mr. Murray:

Physics Safety Sheet—Every safety sheet I’ve ever seen (like mine in Unit 1) are really designed

for Chemistry. I finally found time to write a safety sheet for Physics, which has very particular

safety concerns. I do not have an accompanying worksheet, since I wrote it for my Physics stu-

dents, not IPC. Yet, I thought IPC teachers would appreciate it, too.

Aug 08 Revision of Speed—According to our Math department chair, proportional and indirectly

proportional are not big on TAKS, so I will probably take those references off completely, even-

tually. I did add a second tape timer to show the difference between fast and slow speed. I hope

you have a tape timer to show the students (check with your Physics teacher, if not). A more

modern (and maybe better) way to show linear motion is to use a video camera or a digital cam-

era that has “burst”. The camera I use takes pictures at approximately 0.1 seconds intervals for as

long as I hold down the shutter button. I then show the sequences on the projector. It allows stu-

dents to break down what’s happening, since they can’t really see it in real time. It is also won-

derful for acceleration and projectile motion. For video cameras I believe that one of the new

versions of Media Player can “step” the video.

Variable Sheet—I give out the variable sheet the first day of IPC physics, as well as the TAKS

test equation sheet. (TAKS is the Texas “No Child Left Behind” test.) In actual physics, I give

them an equation sheet, but IPC should not go beyond the basics. Use the variable sheet instead

of making them memorize. Those that do their own work will memorize the units, anyway.

“How to Do Word Problems” and “Practice with Word Problems” - Contrary to logical thinking,

I did not give this out the first day. Instead I waited until after the second day, so that students

were beginning to become frustrated with the math. “How to Do Word Problems” then becomes

relevant.

Study Helps Available —I’m not sure how many of you are aware of the study helps on my

website. There are interactive study helps for you to use for tutoring or an emergency lesson

plan, should you have a computer lab. Check it out. They are as useful as the worksheet.

Maybe more so.

d change of distance s = step 1: variables step 3:...

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