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Velocity-Time Graphs (Edexcel IGCSE Physics)
Revision Note
Velocity-time graphs
- A velocity time graph, or velocity-time graph, shows how the velocity of a moving object varies with time
- Velocity-time refers to the fact that velocity is plotted against time on the graph
- The red line represents an object with increasing velocity
- The green line represents an object with decreasing velocity
Velocity-time graph
Increasing and decreasing velocity represented on a velocity-time graph
Acceleration on a velocity-time graph
- Velocity-time graphs also show the following information:
- Whether the object is moving with a constant acceleration
- The magnitude of the acceleration
- A straight line represents constant acceleration (or deceleration)
- The slope of the line represents the magnitude of acceleration
- A steep slope means large acceleration
- The object's speed changes very quickly
- A gentle slope means small acceleration
- The object's speed changes very gradually
- A positive gradient shows increasing velocity
- The object is accelerating
- A negative gradient shows decreasing velocity
- The object is decelerating
- A flat line means the acceleration is zero
- The object is moving with a constant velocity
- A steep slope means large acceleration
Constant acceleration and constant velocity on a velocity-time graph
Flat horizontal lines on a velocity-time graph show periods of constant velocity, and sloping straight line show periods of acceleration
Gradient of a velocity-time graph
How to find acceleration on a velocity-time graph
- The acceleration of an object can be calculated from the gradient of a velocity-time graph
How to find the gradient of a velocity-time graph
is the change in
(velocity) values
is the change in
(time) values
Worked example
A cyclist is training for a cycling tournament.
The velocity-time graph below shows the cyclist's motion as they cycle along a flat, straight road.
(a) In which section (A, B, C, D, or E) of the velocity-time graph is the cyclist's acceleration the largest?
(b) Calculate the cyclist's acceleration between 5 and 10 seconds.
Answer:
Part (a)
Step 1: Recall that the slope of a velocity-time graph represents the magnitude of acceleration
- The slope of a velocity-time graph indicates the magnitude of acceleration
Therefore, the only sections of the graph where the cyclist is accelerating are sections B and D
- Sections A, C, and E are flat; in other words, the cyclist is moving at a constant velocity (therefore, not accelerating)
Step 2: Identify the section with the steepest slope
- Section D of the graph has the steepest slope
-
Hence, the largest acceleration is shown in section D
Part (b)
Step 1: Recall that the gradient of a velocity-time graph gives the acceleration
- Calculating the gradient of a slope on a velocity-time graph gives the acceleration for that time period
Step 2: Draw a large gradient triangle at the appropriate section of the graph
- A gradient triangle is drawn for the time period between 5 and 10 seconds
Step 3: Calculate the size of the gradient and state this as the acceleration
- The acceleration is given by the gradient, which can be calculated using:
- Therefore, the cyclist accelerated at 1 m/s2 between 5 and 10 seconds
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