Acceleration
Master Acceleration for GCSE Physics with this free worksheet and full mark scheme — Foundation and Higher exam-style questions with worked answers for AQA, Edexcel and OCR. Acceleration is the rate of change of velocity, and for uniform acceleration v² = u² + 2as can be used.
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These worksheets and mark schemes are original, written for Virtus Academy and checked against the current AQA, Edexcel and OCR specifications. Every worksheet comes with a full mark scheme.
Topic overview
Acceleration is the rate of change of velocity. The equation is acceleration = change in velocity ÷ time taken, measured in metres per second squared.
An object slowing down has a negative acceleration, often called deceleration. The change in velocity is the final velocity minus the initial velocity, so a decrease gives a negative value.
A second equation links velocity, acceleration and distance without time: final velocity² − initial velocity² = 2 × acceleration × distance. Near the Earth's surface an object falling freely accelerates at about 9.8 m/s², and an object falling through a fluid reaches a terminal velocity when the resultant force becomes zero.
Revision notes
The equation
Acceleration = change in velocity ÷ time taken, a = Δv ÷ t.
Change in velocity in m/s, time in seconds, acceleration in m/s². Change in velocity is final velocity minus initial velocity.
Deceleration
An object slowing down has a negative acceleration.
Because the change in velocity is final minus initial, a decrease gives a negative value. The magnitude of that negative value is the deceleration.
The uniform acceleration equation
v² − u² = 2as, linking final velocity, initial velocity, acceleration and distance.
This is used when time is not given. Near Earth an object falling freely accelerates at about 9.8 m/s². Terminal velocity is reached when the resultant force becomes zero.
Key points
- Acceleration is the rate of change of velocity.
- Acceleration = change in velocity ÷ time.
- It is measured in m/s².
- Slowing down gives a negative acceleration.
- v² − u² = 2as when time is not given.
- Free fall acceleration is about 9.8 m/s².
Worked examples
Example 1
A car accelerates from 5 m/s to 25 m/s in 4 seconds. Calculate its acceleration. [3 marks]
Model answer
Change in velocity = 25 − 5 = 20 m/s (1 mark). Acceleration = change in velocity ÷ time = 20 ÷ 4 (1 mark) = 5 m/s² (1 mark).
Example 2
A car slows from 20 m/s to 8 m/s in 3 seconds. Calculate its acceleration. [3 marks]
Model answer
Change in velocity = 8 − 20 = −12 m/s (1 mark). Acceleration = −12 ÷ 3 (1 mark) = −4 m/s², a deceleration of 4 m/s² (1 mark).
Example 3
Explain what is meant by terminal velocity. [2 marks]
Model answer
Terminal velocity is the constant velocity reached by an object falling through a fluid (1 mark), when the resultant force on it becomes zero because the drag force equals the weight (1 mark).
Common mistakes
Forgetting the negative sign when decelerating.
Final minus initial gives a negative value when slowing down.
Using the final velocity instead of the change.
The equation needs the CHANGE in velocity.
Giving the unit as m/s.
Acceleration is measured in m/s².
Saying terminal velocity means the object stops.
It means the velocity becomes constant, not zero.
Exam tips
- Calculate the change in velocity as a separate step.
- Keep the negative sign for deceleration.
- Use v² − u² = 2as when time is not given.
- State m/s² as the unit.
Key terms
- Acceleration
- The rate of change of velocity, in m/s².
- Deceleration
- Negative acceleration, when an object slows down.
- Terminal velocity
- The constant velocity when resultant force is zero.
- Free fall
- Falling under gravity alone, at about 9.8 m/s².
Related topics
Written and reviewed against the current AQA, Edexcel and OCR specifications. Spotted an error? Let us know.