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Motion - OCR GatewayDistance-time graphs

Speed and velocity refer to the motion of an object. Distance-time and velocity-time graphs can be a useful way of analysing motion.

Part of Physics (Single Science)Forces

Distance-time graphs

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

A distance time graph shows distance travelled measured by time.

Example

Calculate the speed of the object represented by the green line in the graph, from 0 to 4 seconds (s).

change in distance = (8 - 0) = 8 m

change in time = (4 - 0) = 4 s

\(speed = \frac{distance}{time}\)

\(speed = 8 \div 4\)

\(speed = 2~m/s\)

Question

Calculate the speed of the object represented by the purple line in the graph.

Distance-time graphs for accelerating objects

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.

A graph to show distance travelled by time. A shows acceleration, B shows constant speed, C shows deceleration, and A shows stationary position. Three dotted lines separate each section.

The table shows what each section of the graph represents:

Section of graphGradientSpeed
Aincreasingincreasing
Bconstantconstant
Cdecreasingdecreasing
Dzerostationary (at rest)
Section of graphA
Gradientincreasing
Speedincreasing
Section of graphB
Gradientconstant
Speedconstant
Section of graphC
Gradientdecreasing
Speeddecreasing
Section of graphD
Gradientzero
Speedstationary (at rest)

If an object is accelerating or decelerating, its speed can be calculated at any particular time by:

  1. drawing a tangent to the curve at that time
  2. measuring the gradient of the tangent
A distance x time graph, showing a tangent on a curve.

As the diagram shows, after drawing the tangent, work out the change in distance (A) and the change in time (B).

\(gradient = \frac{vertical~change}{horizontal~change}\)

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.

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Velocity and acceleration
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Average speed and distance

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