Velocity Time Graphs
A velocity-time graph plots an object's velocity against time, so the gradient of the graph gives its acceleration and the area between the graph and the time axis gives the distance travelled. GCSE Higher papers use these graphs to calculate acceleration, deceleration and distances, often by splitting the area into triangles, rectangles and trapeziums.
Before you start
Make sure you're comfortable with these topics first:
Method
- Read the graph carefully, identifying straight sections (constant acceleration or constant velocity) and any curved sections.
- To find acceleration or deceleration over a straight section, calculate the gradient: change in velocity divided by change in time.
- To find distance travelled, calculate the area between the graph and the time axis, splitting the shape into triangles, rectangles or trapeziums as needed.
- Use the trapezium area formula, 0.5 x sum of parallel sides x height, for trapezium sections, and 0.5 x base x height for triangular sections.
- If the graph goes below the time axis, treat that area as negative when finding displacement, but add its magnitude when finding total distance.
- Divide total distance by total time to find the average speed for the whole journey.
Worked example
A cyclist accelerates uniformly from rest to a velocity of 12 m/s in 5 seconds, then travels at this constant velocity for a further 15 seconds, before decelerating uniformly to rest in the final 3 seconds. Calculate the total distance travelled by the cyclist.
- Split the journey into three sections: acceleration (0 to 5 s), constant velocity (5 to 20 s), and deceleration (20 to 23 s).
- Find the area of the acceleration triangle: 0.5 x 5 x 12 = 30 metres.
- Find the area of the constant-velocity rectangle: 15 x 12 = 180 metres.
- Find the area of the deceleration triangle: 0.5 x 3 x 12 = 18 metres.
- Add the three areas together: 30 + 180 + 18 = 228 metres.
- Final answer: total distance travelled = 228 metres.
Practice questions
Try each question, then tap to reveal the answer.
Exam-style questions
Written in the style of a GCSE Maths exam paper, with a full mark scheme.
State what the gradient of a velocity-time graph represents, and state what the area between a velocity-time graph and the time axis represents.
A delivery drone accelerates uniformly from rest to a velocity of 15 m/s in the first 6 seconds, then travels at this constant velocity for a further 10 seconds, before decelerating uniformly to rest over the final 4 seconds. (a) Calculate the total distance travelled by the drone. (b) Calculate the average speed of the drone for the whole journey.
A cyclist accelerates uniformly from rest to reach a velocity of V m/s in 10 seconds, then travels at this constant velocity for a further 15 seconds. The total distance travelled by the cyclist in these 25 seconds is 300 metres. (a) Form an equation in V and solve it to find the value of V. (b) Hence calculate the acceleration of the cyclist during the first 10 seconds.
Free printable worksheet
Want more practice on paper? Download the velocity time graphs worksheet pack - 17 pages of exam-style questions with a full mark scheme. No sign-up, no email wall - just the PDF, free for personal and classroom use.
Build a full practice pack.
This topic is one of hundreds in the library - pick the ones a student needs and generate a printable PDF in minutes.