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Velocity–time graphs – GCSE Maths

Higher · Grade 8 · Calculator

Jump to the questions and answers · Download the worksheet (PDF)

Read acceleration from the gradient and distance from the area under a velocity–time graph, including estimates for curves. It is Higher only, aimed at grade 8. Free questions with answers are on this page. Worked examples show each line before you try the questions.

On a velocity–time graph, gradient is acceleration and area under the line is displacement (distance travelled if the graph stays positive). A horizontal section is constant speed. A straight slope is constant acceleration. Below the time axis is reverse direction — areas then subtract if displacement from the start is asked, but add if total distance is asked.

Estimate a curved graph's area with trapezia. Units: velocity in m/s, time in s, area in metres, gradient in m/s². Do not read a – graph as if it were distance–time (a common mix-up after revising both).

Gradient is acceleration (including deceleration as negative). Area under the graph is displacement. A tangent at a point on a curve estimates instantaneous acceleration. Convert units if the axes are not in m and s.

Objectives

Key points

Worked examples

Example 1

A velocity-time graph is a straight line from 0 m/s to 8 m/s over 6 seconds. Find the distance.

2 marks

  1. The shape is a triangle
  2. Area = 1/2 times 6 times 8
  3. 24

Answer: 24

Common slips
  • Slip: The shape is a rectangle of height 8 It starts at rest, so one end has height 0.
  • Slip: Area = 6 times 8 A triangle is half the rectangle.
  • Slip: 48 Half of 48 is 24.

Example 2

Velocity goes from 4 m/s to 10 m/s in 5 seconds, in a straight line. Find the distance.

2 marks

  1. Both ends are above zero, so use a trapezium
  2. Average speed 7, times 5
  3. 35

Answer: 35

Common slips
  • Slip: Use a triangle of height 10 The starting speed is not zero.
  • Slip: Average speed 10 (4+10)/2 = 7.
  • Slip: 50 7 times 5 is 35.

Example 3

A cyclist holds 5 m/s for 4 seconds, then speeds up steadily to 9 m/s over the next 2 seconds. Find the distance.

3 marks

  1. First piece is a rectangle 5 by 4
  2. Second piece is a trapezium of heights 5 and 9 over 2 seconds
  3. 20 + 14 = 34

Answer: 34

Common slips
  • Slip: First piece is a triangle The speed is constant, so the area is a rectangle.
  • Slip: Second piece is 9 times 2 The speed does not jump to 9 at the start of that piece.
  • Slip: 20 + 18 = 38 Average of 5 and 9 is 7, times 2 is 14.

Questions and answers

GCSE Maths velocity–time graphs questions and answers. Try each one, then open the answer. Easy questions come first.

Question 1 Easy2 marks

From rest to 6 m/s in 10 seconds, in a straight line. What distance is travelled?

Show answer

Answer: 30

  1. Triangle area.
  2. Half of 10 times 6.
  • M1 — Triangle area.
  • A1 — Answer 30

Question 2 Easy2 marks

A constant velocity of 7 m/s is held for 3 seconds. What is the distance?

Show answer

Answer: 21

  1. The graph is a rectangle.
  2. 7 times 3.
  • M1 — The graph is a rectangle.
  • A1 — Answer 21

Question 3 Medium2 marks

From 3 m/s to 7 m/s in 8 seconds, steadily. Find the distance.

Show answer

Answer: 40

  1. Average of 3 and 7.
  2. Times 8.
  • M1 — Average of 3 and 7.
  • A1 — Answer 40

Question 4 Medium2 marks

From 4 m/s to 10 m/s in 5 seconds. Find the acceleration.

Show answer

Answer: 1.2

  1. Change is 6.
  2. 6 divided by 5.
  • M1 — Change is 6.
  • A1 — Answer 1.2

Question 5 Hard2 marks

6 m/s for 3 seconds, then a steady rise to 10 m/s over 4 more seconds. Find the total distance.

Show answer

Answer: 50

  1. Rectangle 6 by 3.
  2. Then a trapezium from 6 to 10 over 4 seconds.
  • M1 — Rectangle 6 by 3.
  • A1 — Answer 50

Question 6 Hard2 marks

The acceleration is 2 m/s^2 from rest. What velocity is reached after 5 seconds?

Show answer

Answer: 10

  1. Velocity change = acceleration times time.
  2. 2 times 5.
  • M1 — Velocity change = acceleration times time.
  • A1 — Answer 10

Question 7 Exam-style5 marks

A runner travels at 4 m/s for 5 seconds, then slows steadily to rest over 5 more seconds. Find the total distance.

Show answer

Answer: 30

  1. First area 4 times 5 = 20.
  2. Second area is a triangle, half of 5 times 4.
  3. That triangle is 10.
  4. Total 30.
  5. Rest means the second shape ends at height 0.
  • M1 — Rectangle
  • A1 — 20
  • M1 — Triangle
  • A1 — 10
  • A1 — Total 30

Common mistakes

Most lost marks on this topic are one slip.

  1. Using the final speed as the distance

    Distance is the area under the graph, not the last reading

  2. Forgetting the half for a triangle or the average for a trapezium

    Use half times base times height, or the average of the two speeds times the time

  3. Dropping the minus sign when the speed falls

    A falling line has a negative gradient, so the acceleration is negative

Spot the slip

A graph goes from 0 m/s to 8 m/s in a straight line. A student says the distance is 8. What did they forget?

  1. The area, not the final speed
  2. The gradient is the distance
  3. Time cannot be read from the axis
Show the slip

The area, not the final speed Distance is the area of the triangle, half times base times height.

Exam tips

Printable worksheet

The same questions are in a PDF you can print. Answers start on a later page.

Download worksheet (PDF)

Or use Print in your browser. Answers under each question are included when you print.

Questions students ask

Is Velocity–time graphs Foundation or Higher?

Velocity–time graphs is Higher only, aimed at grade 8.

What is a common slip on Velocity–time graphs?

Using the final speed as the distance. Distance is the area under the graph, not the last reading.

Where can I get Velocity–time graphs questions and answers?

The questions on this page are free. Open Show answer under each one, or download the worksheet PDF. Start free to practise this topic in the app.

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Last updated 9 November 2026.

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