Edexcel IGCSE Physics · Spec 1.6-1.9
Acceleration and Velocity-Time Graphs
Covers calculate acceleration from velocity change, Interpret the gradient of a velocity-time graph and Distinguish displacement from total distance using graph area.
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Acceleration and Velocity-Time Graphs
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Explained
Velocity time graphs: gradient and area do different jobs
A velocity time graph gives you two separate quantities depending on what you measure. The gradient of the line gives acceleration. The area beneath the line gives distance travelled. Confusing which is which accounts for most lost marks in this topic, so it is worth fixing before anything else.
Acceleration from the gradient
Acceleration is the change in velocity divided by the time taken, measured in metres per second squared. On a graph, that is exactly the gradient: rise over run, with rise in metres per second and run in seconds.
A horizontal line therefore means zero acceleration, which is constant velocity, not being stationary. A straight sloping line means constant acceleration. A curve means the acceleration itself is changing.
Distance from the area
The area under the line gives the distance travelled. Break awkward shapes into rectangles and triangles, work out each, and add them.
The area of a triangle is one half of base times height. Forgetting the half is the single most common arithmetic error here, and it produces an answer exactly twice the correct one.
What examiners say about this topic
Principal examiner reports for Edexcel International GCSE Physics name both traps directly. Common errors are recorded as forgetting the one half factor when calculating triangular areas, and not recognising that distance travelled is given by the area under the graph.
Reports also note confusion between velocity time and distance time graphs, and candidates stating that acceleration changed without describing how or why. If a question asks you to describe motion, say what the velocity is doing and then say what the shape of the line tells you about acceleration.
One further observation is worth having: a large number of candidates drew curved velocity time graphs where air resistance had been ruled out by the question. If the question says to ignore air resistance, the acceleration is constant and the line is straight.
Velocity, not speed
Velocity is speed in a stated direction, so a velocity time graph can go below the axis. A negative velocity means motion in the opposite direction, and the area below the axis counts as displacement in that opposite direction.
That is why total distance and displacement can differ. If a question asks for total distance, add the areas as positive values. If it asks for displacement, treat the area below the axis as negative.
A quick way to check an answer
Look at the units. An acceleration should come out in metres per second squared, and a distance in metres. If you have divided when you should have multiplied, the units of your answer will not match what was asked for, and that is usually quicker to spot than rechecking the arithmetic.
Spec 1.6-1.9
What you need to know
- Calculate acceleration from velocity change
- Interpret the gradient of a velocity-time graph
- Distinguish displacement from total distance using graph area
Active recall
Quick check
Answer each question before opening the answer.
What does graph gradient represent?
Acceleration
What does signed area represent?
Displacement
How is total distance found if velocity is negative?
Add the magnitudes of all separate areas
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