The distance travelled by an object moving at constant speed can be calculated using the equation:
distance travelled = speed × time
This is when:
A car travels 500 m in 50 s, then 1,500 m in 75 s. Calculate its average speed for the whole journey.
First calculate total distance travelled ( ):
500 + 1,500 = 2,000 m
Then calculate total time taken, :
50 + 75 = 125 s
Then rearrange to find :
= 2,000 ÷ 125
= 16 m/s
If an object moves along a straight line, the distance travelled can be represented by a distance-time graph.
Calculate the speed of the object represented by the green line in the graph, from 0 to 4 s.
change in distance = (8 – 0) = 8 m
change in time = (4 – 0) = 4 s
speed = 8 ÷ 4
speed = 2 m/s
Calculate the speed of the object represented by the purple line in the graph.
change in distance = (10 – 0) = 10 m
change in time = (2 – 0) = 2 s
speed = 20 ÷ 2
speed = 5 m/s
Many journeys do not occur at a constant speed. Bodies can speed up and slow down along the journey. However the average speed can still be found for a journey by:
Average speed = total distance travelled ÷ time
Calculate the average speed of the entire journey of the object following the green line on the graph, from 0 s to 7 s.
Average speed = distance ÷ time
Average speed = 8 ÷ 7
Average speed = 1.14 m/s
The table shows what each section of the graph represents:
|Section of graph||Gradient||Speed|
|D||Zero||Stationary (at rest)|
If an object is accelerating or decelerating, its speed can be calculated at any particular time by:
As the diagram shows, after drawing the tangent, work out the change in distance (A) and the change in time (B).
Note that an object moving at a constant speed is changing direction continually. Since velocity has an associated direction, these objects are also continually changing velocity, and so are accelerating.