The movement of objects can be described using motion graphs and numerical values. These are both used to help in the design of faster and more efficient vehicles.

If an object moves along a straight line, the distance travelled can be represented by a distance-time graph.

In a distance-time graph, the gradient of the line is equal to the speed of the object. The greater the gradient (and the steeper the line) the faster the object is moving.

Example

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

Question

Calculate the speed of the object represented by the burgundy-line in the graph, from 0 to 2 s.

change in distance = (10 − 0) = 10 m

change in time = (2 − 0) = 2 s

speed = 10 ÷ 2

The speed of an object can be calculated from the gradient of a distance-time graph.

Distance-time graphs for accelerating objects - Higher

If the speed of an object changes, it will be accelerating or decelerating. This can be shown as a curved line on a distance-time graph.

The table shows what each section of the graph represents:

Section of graph

Gradient

Speed

A

Increasing

Increasing

B

Constant

Constant

C

Decreasing

Decreasing

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).

It should also be noted that an object moving at a constant speed but changing direction continually is also accelerating. Velocity, a vector quantity, changes if either the magnitude or the direction changes. This is important when dealing with circular motion.