Representing motion

The slope on a distance-time graph represents the speed of an object.

The velocity of an object is its speed in a particular direction. The slope on a velocity-time graph represents the acceleration of an object. The distance travelled is equal to the area under a velocity-time graph.

Speed, distance and time

You should recall from your Key Stage 3 studies how to calculate the speed of an object from the distance travelled and the time taken.

The equation

When an object moves in a straight line at a steady speed, you can calculate its speed if you know how far it travels and how long it takes. This equation shows the relationship between speed, distance travelled and time taken:

• For example, a car travels 300 metres in 20 seconds.
• Its speed is 300 ÷ 20 = 15m/s.

Distance-time graphs

You should be able to draw and explain distance-time graphs for objects moving at steady speeds or standing still.

Background information

The vertical axis of a distance-time graph is the distance travelled from the start. The horizontal axis is the time from the start.

Features of the graphs

When an object is stationary, the line on the graph is horizontal. When an object is moving at a steady speed, the line on the graph is straight, but sloped.

The diagram shows some typical lines on a distance-time graph.

Distance - time graph

Note that the steeper the line, the greater the speed of the object. The blue line is steeper than the red because it represents an object moving faster than the one represented by the red line.

The red lines on the graph represent a typical journey where an object returns to the start again. Notice that the line representing the return journey slopes downwards.

Velocity-time graphs

You should be able to explain velocity-time graphs for objects moving with a constant velocity or constant acceleration [acceleration: The rate of change of velocity, measured in metres per second squared. Acceleration = change of velocity ÷ time taken. ].

Background information

The velocity of an object is its speed in a particular direction. This means that two cars travelling at the same speed, but in opposite directions, have different velocities.

The vertical axis of a velocity-time graph…