Question 1 Easy
Velocity rises from 2 m/s to 8 m/s in 4 seconds. Find the acceleration.
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Answer: 1.5
- Change in velocity is 6.
- Divide by 4.
- Method (1): Change in velocity is 6.
- Accuracy (1): Answer 1.5
Velocity–time graphs practice questions with answers
A second set of velocity–time graphs questions for GCSE Maths. They are different from the ones on the topic page, so work through both. Try each question, then open the answer to check your working.
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Question 2 Easy
Velocity falls from 8 m/s to 0 in 4 seconds. Find the acceleration.
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Answer: -2
- The change is negative.
- -8 divided by 4.
- Method (1): The change is negative.
- Accuracy (1): Answer -2
Question 3 Medium
A car slows from 12 m/s to 4 m/s in 4 seconds. Find the acceleration.
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Answer: -2
- Change is -8.
- Divide by the time.
- Method (1): Change is -8.
- Accuracy (1): Answer -2
Question 4 Medium
Rest to 12 m/s in 4 seconds, straight line. State the distance.
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Answer: 24
- Half times 4 times 12.
- That is 24.
- Method (1): Half times 4 times 12.
- Accuracy (1): Answer 24
Question 5 Hard
A graph shows acceleration -1.5 m/s^2 for 4 seconds, starting at 9 m/s. What is the final velocity?
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Answer: 3
- Change = -1.5 times 4.
- Subtract that from 9.
- Method (1): Change = -1.5 times 4.
- Accuracy (1): Answer 3
Question 6 Hard
A straight line on a velocity-time graph goes from 0 m/s to 10 m/s in 8 seconds. Find the distance travelled.
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Answer: 40
- This is a triangle, because it starts from rest.
- Half of 8 times 10 is 40.
- Method (1): This is a triangle, because it starts from rest.
- Accuracy (1): Answer 40
Exam-style question
A longer question with marks, in the style of a written paper. This is a Yumio practice question, not a past paper question.
Exam-style question 14 marks
A velocity-time line runs from 2 m/s to 8 m/s in 4 seconds. Find the acceleration and the distance.
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Answer: 1.5 and 20
- Acceleration is 6/4 = 1.5.
- Distance uses the average speed 5.
- 5 times 4 = 20.
- Method (1): Change in velocity
- Accuracy (1): Acceleration 1.5
- Method (1): Average speed
- Accuracy (1): Distance 20
Quick checks
Short one-step questions. Pick an option before you open the answer.
Check 1
On a velocity-time graph, what is the gradient?
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Acceleration. It is the change in velocity divided by time. Acceleration. It is the change in velocity divided by time.
Check 2
On a velocity-time graph, what is the area?
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Distance travelled. Distance travelled.
Check 3
Why is a start from rest a triangle?
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One end of the shape has height zero. One end of the shape has height zero.
Check 4
Why is a non-zero start and end a trapezium?
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Both vertical ends have height, so you average them. Both vertical ends have height, so you average them.
Check 5
A negative gradient means what?
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The object is slowing down if velocity stays positive. The acceleration is negative. The object is slowing down if velocity stays positive. The acceleration is negative.
Check 6
Units of the area when velocity is in m/s and time in seconds?
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Metres (m). Multiplying m/s by s leaves metres. Metres (m). Multiplying m/s by s leaves metres.
Check 7
How do you split a flat section followed by a slope?
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A rectangle, then a trapezium or triangle, then add. A rectangle, then a trapezium or triangle, then add.
Check 8
Is the final velocity the same as the distance?
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No. Distance is the area, not the last reading on the vertical axis. No. Distance is the area, not the last reading on the vertical axis.
Check 9
Average of 4 m/s and 10 m/s is what?
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7 m/s. Multiply by time to get distance for a straight change. 7 m/s. Multiply by time to get distance for a straight change.
Check 10
Half times base times height is for which region?
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A triangle, including a straight run up from rest. A triangle, including a straight run up from rest.
Check 11
A horizontal line on the graph means what acceleration?
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Zero. The velocity is not changing. Zero. The velocity is not changing.
Check 12
From 8 m/s to 0 in 4 seconds, what is the acceleration?
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-2 m/s^2. -2 m/s^2.
Check 13
Can distance be read from a curved velocity graph?
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Yes, as the area, but a curve needs splitting or counting, not one triangle formula. Yes, as the area, but a curve needs splitting or counting, not one triangle formula.
Check 14
What is 1/2 times 6 times 8?
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24. That is the triangle from 0 to 8 in 6 seconds. 24. That is the triangle from 0 to 8 in 6 seconds.
Check 15
Why add the areas of two pieces?
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Each piece is part of the journey. The total distance is the sum. Each piece is part of the journey. The total distance is the sum.
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