Area under a graph

The Maths Habit Handout to print

A runner starts from standing still and speeds up steadily to 8 m/s in 4 seconds. Does she run more or less than 32 m?

Less: she is slower than 8 m/s nearly all the time

Velocity-time graph
Shows how fast something is moving as time passes.
Area under the graph
The space between the graph and the time axis. It gives the distance travelled.

Area under the graph = distance travelled

Work out the area

triangle: base 6, height 4 12

How far does it travel?

10 m/s for 4 seconds 40 m

Find the distance travelled.

Find the distance travelled.

Find the distance travelled.

area under the graph = distance
A =½ × 4 × 10 = 20
B =6 × 10 = 60
Distance80m

Find the distance travelled.

A =½ × 2 × 8 = 8
B =5 × 8 = 40
Distance48m

Find the distance travelled.

area under the graph = distance
A =½ × 4 × 10 = 20
B =6 × 10 = 60
Distance80m

Find the distance travelled.

A =½ × 3 × 12 = 18
B =4 × 12 = 48
C =½ × 3 × 12 = 18
Distance84m

Area under a graph worksheet, page 1

Area under a graph worksheet, page 2

Answer sheet

  1. A car speeds up steadily from 0 to 20 m/s in 8 seconds, then stays at 20 m/s. How long after setting off has it travelled 200 m?

    14 seconds

  2. A car speeds up steadily from 6 m/s to 14 m/s in 10 seconds. How far does it travel?

    100 m

  1. How far does the cyclist travel in the 6 seconds?

    36 m
    012345604812Time (s)Velocity (m/s)

  2. Find the distance travelled.

    68 m
    02468101202468Time (s)Velocity (m/s)

  3. A car speeds up steadily from 4 m/s to 10 m/s in 6 seconds. How far does it travel?

    42 m
Exit tickets to print