Speed, velocity and acceleration

Motion

• When an object changes its position, motion has occurred.– Distance- How far an object has moved.– Displacement- How far an object has moved in

relation to its starting point.– Consider direction

Example: Two runners travel along the same straight path in a straight line for 500 meters. At the end of the run their distances are the same but their displacements are different. How can this be so?

1 Both Mr Rabbit and Mr Tortoise took the same round trip, but Mr Rabbit slept & returned later.

Comment on their their argument.

Me, as I spent less time on the

trip.

No, I travelled longer distance every

minute.

Who runs faster?

SPEED Distance an object travels per unit of time

Relationships between speed, distance, and time:

Speed = Distance/ Time = d/ t » Constant Speed- speed does not change over

time» Average Speed- speed of motion when speed

is changing

Avg Speed = Total Distance/ Total Time

» Instantaneous Speed- speed at any given moment in time (speedometer)

SpeedHow can we describe how fast an object moves?A car on Tolo Highway

travels 90 km in 1 hour. We say that the car travels at a speed of 90 km/h.

SpeedSpeed is a measure of how fast

something moves.

Speed = distance travelled per unit of time

Speed = distance travelled per unit of time

SI unit: m/s or km/h (for long distances)

How can we describe how fast an object moves?

KINDS OF SPEED

Average, Instantaneous, Constant

and speeds up again to 60 km/hand speeds up again to 60 km/h

Average speed

Its average speed over the whole journeyoverall distance travelled

total time of travel

slows down to 0 km/hslows down to 0 km/h

A car travels at 50 km/hA car travels at 50 km/h

=

Average speed does not tell the variations during the journey.

On most trips, the speed at any instant is often different from the

average speed.

Instantaneous speedspeed at any instant

The word ‘speed’ alone instantaneous speed

Instantaneous speed distance travelled in an extremely

short time interval

Simulation

Speedometer tells the car’s speed at any instant!

Instantaneous speed

Constant Speed Elapsed time

(seconds)Distance (meters)

0 0

2 4

4 8

6 12

8 16

10 20

12 24

Not changing

speed. Same

amount of speed from beginning

to last.

Motion Graphs – Position vs. Time

constant, rightward (+) velocity of +10 m/s

a rightward (+), changing velocity - that is, a car that is moving rightward but speeding up or accelerating

Graphing Motion

• Graph distance on the y-axis and time on the x-axis

Slope = rise = distance = speed run time

Distance - Time Graph

• If something is not moving, a horizontal line is drawn.

• If something starts out slow and then speeds up, its change in speed can look like this.

Learning Checkpoint

This graph shows several stages of motion:

• Stage 1: 100 m in 10 s

• Stage 2: 50 m in 10 s

• Stage 3: 150 m in 20 s

Calculate the speed as indicated by each of the colors.

Calculate the average speed.

What is the total distance?

What is the displacement?

Solution

Stage 1: S= d/ t100 m/ 10 s= 10 m/s

Stage 2: S= d/t50 m/ 10 s= 5 m/s

Stage 3: S= d/t150 m/ 20 s= 7.5 m/s

Ave Speed= Tot d/ Tot t300 m/ 40 s= 7.5 m/s

Distance = 300 metersDisplacement = 0 meters

KINDS OF VELOCITY

Average, Instantaneous, Constant

Velocity

rate of change of displacement. a speed in a given direction or

velocitya

vector quantit

y

direction

magnitude(speed)

Velocity is...

speed = 300 km/hdirection = west

Train drivers concern speed only.

Speed with direction

Pilots concern velocity (direction & speed).

speed = 90 km/h

Average velocity

Average velocity =overall displacement

total time of travel

direction of velocity = direction of overall displacement

Instantaneous velocity

The velocity at any instant is called instantaneous velocity.

If a car moves at a constant velocity...

… its average and instantaneous velocities have the same value.

Constant VELOCITYElapsed time

(seconds)Distance (meters)

0 0

2 4

4 8

6 12

8 16

10 20

12 24

Not changing

speed. Same

amount of speed from beginning

to last.

Graph: Constant VelocityDistance vs. Time

0

2

4

6

8

10

12

14

0 5 10 15 20 25 30

Time

Dis

tan

ce

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

Velo

city

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

Terminal Velocity

Terminal velocity- the velocity at which the upward force of air resistance equals the downward force of gravity.

Once you reach this velocity you will no longer accelerate. (just stay at the same velocity)

Parachutes increase your surface area to increase your air resistance in order to reduce your terminal velocity so you don’t die when you hit the ground.

Velocity Questions

1) How far does Bob run if he maintains an average velocity of 3 m/s for 10 s?

2) List three ways you can change the velocity of your car.

3) Is it possible to go around a corner without changing velocity? Explain.

4) One car is going 25 miles/hr north, another car is going 25 miles/hr south. Do they have the same velocity? Explain.

Q1 The world record...

( )Average speed = 10.49

= 9.53 m/s or 34.3 km/h

100

The world record of women 100-m race is 10.49 s.

What is the average speed?

In an orienteering event, Maria and Karen reach their control points at the same time.

Q2 In an orienteering event...

start, 10:00 amstart, 10:00 amMaria, 10:30 amMaria, 10:30 am

Karen, 10:30 amKaren, 10:30 am

Who runs in a higher average velocity?Who runs in a higher average velocity?

A Maria.

B Karen.

C Undetermined since their paths are unknown.

D Incomparable since they run along different directions.

Who runs in a higher average velocity?Who runs in a higher average velocity?

Q2 In an orienteering event...

Note: The distance travelled is equal to magnitude of displacement only if it is a straight-line motion. Speed is usually larger than the magnitude of velocity.

Q3 True or false:

(T/F)

Average speed of an object magnitude of its average velocity.

A man takes a walk starting from rest and ending at rest.

Q4 True or false:

(T/F)

It is possible for him to attain an average speed of 5 km h–1 but he never goes faster than 5 km h–1.

ACCELERATION

Acceleration measures the change in velocity

Acceleration = velocity per unit time

Acceleration = velocity per unit time

direction

speed

overall change in velocitytotal time taken

= m/s2Unit: m/s / s vector quantity

=

AccelerationWhen a car moves faster and faster, its speed is increasing (velocity changed).

DEceleration

When a car moves slower and slower,

its speed is decreasing (- velocity changed).

When a car changes direction,

its velocity changes too.

Acceleration

• If you have starting and ending velocity or speed, find that before you use the triangle.

• If not, use triangle to find change in velocity (Dv), then find initial or final velocity

• Dv = ending velocity – starting velocity

Solving Acceleration Problems using Acceleration Triangle

a

Dv

t

If a car accelerates at 2 m/s, what does that mean?

3 Acceleration

t = 1 sv = 2 m/s,v = 2 m/s

v = 0

t = 2 sv = 4 m/s, v = 2 m/s

v = 6 m/s, v = 2 m/s

t = 3 s

1 m

t = 0

3 m

5 m

Acceleration at constant speed

• An object moving in a circle at constant speed is always

accelerating (changing direction).

Motion Graphs – Velocity vs. Time

constant, rightward (+) velocity of +10 m/s

a rightward (+), changing velocity - that is, a car that is moving rightward but speeding up or accelerating

Acceleration Questions

1) A dragster going at 10 m/s increases its velocity to 25 m/s in 4 seconds. What is its acceleration?

2) The driver of a car steps on the brakes, and the velocity drops from 20 m/s to 8 m/s in a time of 2 seconds. Find his acceleration.

3) Find the acceleration of a car that travels at a constant velocity of 40 Km/hr for 10 s.

4) Challenge: Calculate the velocity of a skateboarder who accelerates from rest for 4 seconds down a ramp at an acceleration of 5 m/s2.

Uniform Acceleration : Velocity vs. Time

Velocity Time Graph: Uniform Acceleration

0

2

4

6

8

10

12

14

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

• What is the magnitude of the object’s total displacement after 4 seconds

• What is the average speed after 3 seconds?

Graph Question

8m

V= d/t

V= 8m/3s

V= 2.66 m/s

Summary• Distance and time measurements can be used to

describe the velocity and acceleration• The Shape of the Distance vs. Time determines the type of motion

– Rest : Straight line parallel to time axis– Constant Speed : Straight line on a slope (magnitude of the

speed)– Constant Acceleration: Curved line

• The Shape of the Velocity vs. Time determines the type of motion– Rest : Straight line on the time axis– Constant Speed : Straight line parallel to the Time axis– Constant Acceleration: Straight line on a slope (magnitude of the

Acceleration)

Q1 A running student...

A running student is slowing down in front of a teacher. With reference to the sign convention,

Acceleration of student: positive / negative

Velocity of student: positive / negative

+ve

Quantity Unit Scalar/Vector

Speed ______ _____

Velocity ______ _____

Change in velocity ______ _____

Acceleration ______ _____

Q2 When time is measured...

Unit of time: hour (h)

km h–1

km h–1

km h–1

km h–2

scalarvectorvectorvector

Unit of distance/displacement: kilometer (km)