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1- D Motion Kinematics“Motion in a

Straight Line!”

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KINEMATICS•- the process of motion is integral to the description of matter characteristics!

•- all matter is moving - therefore a method must be formulated for accuracy!

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Describe motion in a straight line

Which car has the greatest velocity? BLUE

Which car has a constant velocity? RED

Which 2 cars have the same average velocity?

RED and GREEN

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DISTANCE vs. DISPLACEMENT

•1. DISTANCE - defined as the magnitude or length of motion - NO DIRECTION INDICATED symbol = d

•2. DISPLACEMENT - magnitude and direction of motion symbol = s

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Speed

Speed: The “rate” of change of distance covered.

A rate is anything compared to time.

In own words, how “fast”.

distance

Speed = -----------------

time

Typical units: mi/hr, km/hr, m/s...

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Average Speed

Total distance covered

Average speed = --------------------------

total time

SPEED

d

t

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Instantaneous Speed:

The speed of an object at any particular instant.

The average speed and instantaneous speed may not be the same!

A car that gradually speeds up more and more has an instantaneous speed

that always changes..

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Constant Speed

An object could be moving at a steady rate.

Thus, its average and instantaneous speed would be the same!

GBS Physics - speed vs. velocity

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SOME EXAMPLES

• 1. A motocross rider travels a total distance of 300 km during a race. It takes the rider 2.5 hours to travel this distance. What is the average speed of the rider?

SOLUTION: AVE SPEED = Total Distance / time

speed = 300 km / 2.5 hrs = 120 km/hr

v

d

t

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SOME EXAMPLES

speed = 454 km / 7200s = 454000m / 7200s

= 63 m/s

v

d

t

• A high speed train travels 454 km in 7200 seconds. What is the train’s average speed?

• Formula : v (speed) = d/t

d

t

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Velocity

Velocity and speed are often used interchangeably. They are not the

same term though!

Speed is a scalar quantity. It has a number value only. No direction.

Velocity is a vector quantity. It has a size and direction.

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Question:A car is traveling at a constant 60mi/hr in a

circular path.

Does it have a constant speed?Does it have a constant velocity?

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AccelerationAcceleration: The rate of change in speed

and/or direction (or velocity)How fast something speeds up, slows down, or

turns.

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If an object has a constant velocity, then its acceleration would be zero.

If an object is slowing down, it is decelerating:

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change in velocity

acceleration = ------------------------

time interval Δv

a = ----------- Δt

Δ, Greek letter delta = change in

GBS Physics - Acceleration

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Change in Speed/Velocity

Acceleration = --------------------------

total time

Acc

v

t

Eq: a = ∆v or a = vf – vi ∆t tf - ti

Units m , km, mi, ft, s2 h.s h.s s2

Always a distance unit divided by two units of

time. Why?

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Ex: A particular car goes from rest to 90km/hr in 10 sec, what is its acceleration?

Δv = 90 km/hr Δt = 10 sec a = Δv/ Δt

= 90 km/hr/10 sec=9 km/hr / secnotice units...

This means its velocity is changing by 9km/hr every second it accelerates at that rate.

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Velocity vs. Acceleration?

If you are flying at a constant 500 mi/hr on a jet airplane, do you have a large velocity? A large

acceleration?

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• 2. The stealth fighter accelerates from 700 mph to 1200 mph in 10 seconds. What is the acceleration of the aircraft?

Acceleration = change in velocity / time

(1200 mph - 700 mph) / 10 s

50 mph/s

(500 mph) / 10 s =

Acc

v

t

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• 3. A toy car accelerates from rest to a speed of 100 m/s in 5 seconds. What is the acceleration?

Acceleration = change in velocity / time

(100 m/s - 0 m/s) / 5 s

20 m/s/s or 20 m/s2

40m-20m

4 s-2 s= 20m / 2s = 10 m/s

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GRAPHICAL REPRESENTATION OF VELOCITY

•slope - the slope of a displacement vs. time curve would be the velocity

• Time is always the independent or x-axis.• Plot points and draw a line of best fit. • Remember! Label axis with units, and title graph.

• DO NOT CONNECT DOTS!GBS Physics - position vs. time

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Data Chart : Constant Velocity

Elapsed time (seconds) Distance (meters)

0 0

2 4

4 8

6 12

8 16

10 20

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Copy the data chart and construct Copy the data chart and construct a Distance vs. Time Grapha Distance vs. Time Graph

Answer on the next SLIDEAnswer on the next SLIDE

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Graph: Constant VelocityDistance vs. Time

0

2

4

6

8

10

12

14

0 5 10 15 20 25 30

Time

Dis

tan

ce

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Data Chart

Constant Acceleration!What type of motion?

Elapsed time

(seconds)Distance (meters)

0.0 0

4.0 8

8.0 32

12.0 72

16.0 128

20.0 200

24.0 288

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Graph of Data: Constant Acceleration

Constant Acceleration

0

50

100

150

200

250

300

350

0.0 5.0 10.0 15.0 20.0 25.0 30.0

time

Dis

tan

ce

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Constant VelocityPositive Velocity

Positive VelocityChanging Velocity (acceleration)

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Fast, Rightward (+)

Constant Velocity

                                                    

http://www.physicsclassroom.com/mmedia/kinema/cpv.html

Fast, Leftward (-)

Constant Velocity

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GRAPHICAL REPRESENTATION OF ACCELERATION

•slope - the slope of a velocity vs. time curve would be the acceleration

GBS Physics - velocity vs time

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Velocity Time GraphElapsed

time (seconds)

Distance (meters)

Velocity (m/s)

0 0.0 0.0

2 4.0 2.0

4 8.0 2.0

6 12.0 2.0

8 16.0 2.0

10 20.0 2.0

12 24.0 2.0

Velocity vs Time

0

0.5

1

1.5

2

2.5

0 5 10 15

Time

Vel

ocity

Copy the data chart and construct a VELOCITY vs. Copy the data chart and construct a VELOCITY vs. TIME GraphTIME Graph

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Uniform Acceleration : Velocity vs. Time

Velocity Time Graph: Uniform Acceleration

0

2

4

6

8

10

12

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0.0 5.0 10.0 15.0 20.0 25.0 30.0

Time

Vel

oci

ty

Elapsed time

(seconds)Distance (meters)

0.0 0

4.0 8

8.0 32

12.0 72

16.0 128

20.0 200

24.0 288

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Positive VelocityPositive Acceleration

Positive VelocityZero Acceleration

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