Distance-Time Graphs (CIE IGCSE Physics: Co-ordinated Sciences (Double Award))

• A distance-time graph is used to describe the motion of an object and calculate its speed

Distance-time graph of an object moving at a constant speed

The graph shows a moving object moving further away from its origin at a constant speed

Constant speed on a distance-time graph

• If an object is moving at a constant speed, the distance-time graph will be a straight line
  • If the constant speed is zero, the line will be horizontal
  • If the constant speed is non-zero, the line will have a gradient

• If an object has a speed of zero, the object is stationary
  • The distance moved by the object over time is zero

• The gradient of a distance-time graph represents the magnitude of the object's velocity, or its speed
  • A steeper slope, or a higher gradient, represents a greater speed
  • A shallower slope, or a lower gradient, represents a slower speed

Different speeds on a distance-time graph

Both of these objects are moving at a constant speed, because the lines are straight. The steeper slope represents the faster speed and the shallower line represents the slower speed.

Changing speed on a distance-time graph

• Often, the speed of an object is not constant
• If the speed of an object is changing, the object is accelerating
• If an object is accelerating, the distance-time graph will be a curved line

• A curve on a distance-time graph is a changing gradient
  • If the gradient increases over time, the speed is increasing over time
  • If the gradient decreases over time, the speed is decreasing over time

Speed of an object increasing and decreasing on a distance-time graph

Changing speeds are represented by changing slopes, or gradients. The red line shows a decreasing gradient and represents an object slowing down, or decelerating. The green line shows an increasing gradient and represents an object speeding up, or accelerating.

• The speed of a moving object can be calculated from the gradient of the line on a distance-time graph:

The speed of an object can be found by calculating the gradient of a distance-time graph

•  is the change in y (distance) values
•  is the change in x (time) values