Velocity-time graphs

Edexcel Statements

Velocity-time graph

• What story does the graph tell?

0 20 40 60 80 100 1200

10

20

30

40

50

60

Time/s

Velocity(m/s)

Finding the accelerationWe know that

Gradient of a graph

velocity

Time

Change in velocity

Change in time

So the gradient of a velocity time graph gives the acceleration

The steeper the gradient the greater acceleration

0 10 20 30 40 50 60 70 80 90 100 1100

10

20

30

40

50

60

Time/s

Velocity m/s

What if the gradient is zero?

Velocity

Time

A horizontal line means that the object has a constant (or uniform) velocity.

What if the slope is negative?

Velocity

Time

Calculating the average velocity

average   velocity  = initial   velocity+final   velocity

2

or

Example 1A car accelerates uniformly from rest for 10 seconds, to then travels at a constant velocity for 20s. Then the driver brakes hard and comes to a complete stop in 2s.

Sketch the velocity – time graph

Velocity(m/s)

Time (s)

The area under a velocity-time graph gives the distance travelled

velocity = distance  time

distance  =  velocity  × time

Velocity(m/s)

Time (s)

Example 2

• Plot a velocity-time graph using the data given

Velocity (m/s)

0.0 2.0 4.0 8.0 12.0 12.0 12.0 12.0 12.0

Time (s) 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0

Draw a line of best fit for each section and use the graph to finda) The acceleration in the first 2 secondsb) The acceleration between 2.0 and 3.0 secondsc) The total distance travelled d) The average speed for the 8 seconds

0 1 2 3 4 5 6 7 8 90

2

4

6

8

10

12

14

Time (s)

Velocity (m/s)

Summary

• The gradient of a velocity-time graph gives the acceleration.

• A steeper gradient means that the object is accelerating faster

• A zero gradient (a horizontal line) means the object is travelling at a constant velocity

• A linear graph/section shows that the acceleration is constant

• If any section of the graph is curved, then the acceleration is changing and is no longer constant.