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Variable acceleration

Past-paper questions pack

Name
Class
Date set
Date due
Score/ 131

Questions are numbered; the mark schemes (the answer key) follow on separate pages so the question pages can be handed out alone. www.mathsaleveltutor.com

Edexcel AS and A-level Maths past-paper questions since June 2018 · 37 parts, 131 marks · mark schemes follow the questions · www.mathsaleveltutor.com · Questions and mark schemes © Pearson Education Ltd

1. June 2025 · AS Paper 2 (Mechanics) · Q4(a) · 4 marks
4. In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. A fixed point O lies on a straight line. A particle P moves along the straight line. At time t seconds, t 0, the distance, s metres, of P from O is given by 3 – 12t 2 + 18t s = 2t (a) Find the values of t for which P is instantaneously at rest. (4)
2. June 2025 · AS Paper 2 (Mechanics) · Q4(b) · 3 marks
(b) Find the total distance travelled by P in the interval 0 t 4 (3)
3. June 2025 · AS Paper 2 (Mechanics) · Q4(c) · 3 marks
(c) Find the maximum speed of P in the interval 1 t 3 (3)
4. June 2025 · Paper 3 (Mechanics) · Q4(c) · 2 marks
(c) Find an expression for the velocity of P at time t seconds, where t > 0, giving your answer in terms of t, i and j (2)
5. June 2025 · Paper 3 (Mechanics) · Q4(d) · 4 marks
At t = T, the acceleration of P is in a direction that is perpendicular to the line with equation y = 3 x (d) Find the value of T. (4)
6. June 2024 · AS Paper 2 (Mechanics) · Q2(a) · 3 marks
2. In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable. A particle is moving along a straight line. At time t seconds, t > 0, the velocity of the particle is vms-1, where v t t (a) Find the acceleration of the particle when t = 4 (3)
7. June 2024 · AS Paper 2 (Mechanics) · Q2(b) · 4 marks
When t = 1 the particle is at the point X. When t = 2 the particle is at the point Y. Given that the particle does not come to instantaneous rest in the interval 1 < t < / (b) show that XY O 28 2 metres. 3 41 (4)
8. June 2024 · Paper 3 (Mechanics) · Q4(b) · 4 marks
(b) Find the speed of P when t = 4 (4)
9. June 2024 · Paper 3 (Mechanics) · Q4(c) · 4 marks
When t = T, P is accelerating in the direction of (–i – 27j). (c) Find the value of T. (4)
10. June 2023 · AS Paper 2 (Mechanics) · Q3(a) · 1 marks
3. In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. A fixed point O lies on a straight line. A particle P moves along the straight line such that at time t seconds, t 0, after passing through O, the velocity of P, v m s –1, is modelled as 2 – 2t v = 15 – t (a) Verify that P comes to instantaneous rest when t = 3 (1)
11. June 2023 · AS Paper 2 (Mechanics) · Q3(b) · 3 marks
(b) Find the magnitude of the acceleration of P when t = 3 (3)
12. June 2023 · AS Paper 2 (Mechanics) · Q3(c) · 4 marks
(c) Find the total distance travelled by P in the interval 0 t 4 (4)
13. June 2023 · Paper 3 (Mechanics) · Q3(c) · 2 marks
(c) the acceleration of P at time t seconds (2)
14. June 2023 · Paper 3 (Mechanics) · Q3(d) · 2 marks
(d) the value of t when the direction of the acceleration of P is perpendicular to i (2)
15. June 2022 · AS Paper 2 (Mechanics) · Q3(a) · 6 marks
3. A fixed point O lies on a straight line. A particle P moves along the straight line. At time t seconds, t 0, the distance, s metres, of P from O is given by s = 1 3 - 5 2 + 6t 3 t 2 t (a) Find the acceleration of P at each of the times when P is at instantaneous rest. (6)
16. June 2022 · AS Paper 2 (Mechanics) · Q3(b) · 3 marks
(b) Find the total distance travelled by P in the interval 0 t 4 (3)
17. June 2022 · Paper 3 (Mechanics) · Q1(b) · 2 marks
(b) Find an expression, in terms of t, i and j, for the acceleration of P at time t seconds, where t > 0 (2)
18. June 2022 · Paper 3 (Mechanics) · Q1(c) · 4 marks
At time t = 4 seconds, the position vector of P is (i – 4j) m. (c) Find the position vector of P at time t = 1 second. (4)
19. Oct 2021 · AS Paper 2 (Mechanics) · Q2(a) · 2 marks
2. A particle P moves along a straight line. At time t seconds, the velocity v m s-1 of P is modelled as v = 10t - t 2 - k t 0 where k is a constant. (a) Find the acceleration of P at time t seconds. (2)
20. Oct 2021 · AS Paper 2 (Mechanics) · Q2(b) · 4 marks
The particle P is instantaneously at rest when t = 6 (b) Find the other value of t when P is instantaneously at rest. (4)
21. Oct 2021 · AS Paper 2 (Mechanics) · Q2(c) · 4 marks
(c) Find the total distance travelled by P in the interval 0 t 6 (4)
22. Oct 2021 · Paper 3 (Mechanics) · Q5(a) · 2 marks
5. At time t seconds, a particle P has velocity v m s-1, where 2 i - 2t j t > 0 v = 3t (a) Find the acceleration of P at time t seconds, where t > 0 (2)
23. Oct 2021 · Paper 3 (Mechanics) · Q5(b) · 3 marks
(b) Find the value of t at the instant when P is moving in the direction of i - j (3)
24. Oct 2021 · Paper 3 (Mechanics) · Q5(c) · 3 marks
At time t seconds, where t > 0, the position vector of P, relative to a fixed origin O, is r metres. When t = 1, r = -j (c) Find an expression for r in terms of t. (3)
25. Oct 2021 · Paper 3 (Mechanics) · Q5(d) · 6 marks
(d) Find the exact distance of P from O at the instant when P is moving with speed 10 m s-1 (6)
26. Oct 2020 · AS Paper 2 (Mechanics) · Q3(a) · 4 marks
3. A particle P moves along a straight line such that at time t seconds, t 0, after leaving the point O on the line, the velocity, v m s–1, of P is modelled as v = (7 – 2t)(t + 2) (a) Find the value of t at the instant when P stops accelerating. (4)
27. Oct 2020 · AS Paper 2 (Mechanics) · Q3(b) · 5 marks
(b) Find the distance of P from O at the instant when P changes its direction of motion. (5)
28. Oct 2020 · Paper 3 (Mechanics) · Q3(i)(a) · 3 marks
3. (i) At time t seconds, where t 0 , a particle P moves so that its acceleration a m s-2 is given by a = (1 - 4t) i + (3 - t2) j At the instant when t = 0, the velocity of P is 36i m s-1 (a) Find the velocity of P when t = 4 (3)
29. Oct 2020 · Paper 3 (Mechanics) · Q3(i)(b) · 3 marks
(b) Find the value of t at the instant when P is moving in a direction perpendicular to i (3)
30. Oct 2020 · Paper 3 (Mechanics) · Q3(ii) · 6 marks
(ii) At time t seconds, where t 0 , a particle Q moves so that its position vector r metres, relative to a fixed origin O, is given by r = (t2 - t) i + 3t j Find the value of t at the instant when the speed of Q is 5 m s-1 (6)
31. June 2019 · AS Paper 2 (Mechanics) · Q3(a) · 5 marks
3. A particle, P, moves along a straight line such that at time t seconds, t . 0, the velocity of P, v m s–1, is modelled as v = 12 + 4t – t2 Find (a) the magnitude of the acceleration of P when P is at instantaneous rest, (5)
32. June 2019 · AS Paper 2 (Mechanics) · Q3(b) · 3 marks
(b) the distance travelled by P in the interval 0 - t - 3 (3)
33. June 2019 · Paper 3 (Mechanics) · Q1(a) · 3 marks
1. [In this question position vectors are given relative to afixed origin O| At time ¢ seconds, where ft > 0, a particle, P, moves so that its velocity vms! is given by 3 v = 6f1 -— 5Pj When f= 0, the position vector ofP is (—20i + 20j)m. (a) Find the acceleration of P when ¢ = 4 (3)
34. June 2019 · Paper 3 (Mechanics) · Q1(b) · 3 marks
(b) Find the position vector of P when ¢ = 4 (3)
35. June 2018 · AS Paper 2 · Q8(a) · 5 marks
8. A particle, P, moves along the x-axis. At time t seconds, t . 0, the displacement, x metres, of P from the origin O, is given by x = t ( t - t + ) (a) Find the times when P is instantaneously at rest. (5)
36. June 2018 · AS Paper 2 · Q8(b) · 3 marks
(b) Find the total distance travelled by P in the time interval 0 - t - 2 (3)
37. June 2018 · Paper 3 · Q6 · 6 marks
6. At time t seconds, where t 0, a particle P moves in the x-y plane in such a way that its velocity v m s-1 is given by -1 2 i - 4tj v = t When t = 1, P is at the point A and when t = 4, P is at the point B. Find the exact distance AB. (6)

Mark schemes

Each mark scheme shows the whole question; the parts on this topic are the ones listed above.

June 2025 · AS Paper 2 (Mechanics) · Q4
Mark scheme June 2025 Paper 2 (Mechanics) Q4(c)
June 2025 · Paper 3 (Mechanics) · Q4
Mark scheme June 2025 Paper 3 (Mechanics) Q4(d)
June 2024 · AS Paper 2 (Mechanics) · Q2
Mark scheme June 2024 Paper 2 (Mechanics) Q2(b)
June 2024 · Paper 3 (Mechanics) · Q4
Mark scheme June 2024 Paper 3 (Mechanics) Q4(c)
June 2023 · AS Paper 2 (Mechanics) · Q3
Mark scheme June 2023 Paper 2 (Mechanics) Q3(c)
June 2023 · Paper 3 (Mechanics) · Q3
Mark scheme June 2023 Paper 3 (Mechanics) Q3(d)
June 2022 · AS Paper 2 (Mechanics) · Q3
Mark scheme June 2022 Paper 2 (Mechanics) Q3(b)
June 2022 · Paper 3 (Mechanics) · Q1
Mark scheme June 2022 Paper 3 (Mechanics) Q1(c)
Oct 2021 · AS Paper 2 (Mechanics) · Q2
Mark scheme Oct 2021 Paper 2 (Mechanics) Q2(c)
Oct 2021 · Paper 3 (Mechanics) · Q5
Mark scheme Oct 2021 Paper 3 (Mechanics) Q5(d)
Oct 2020 · AS Paper 2 (Mechanics) · Q3
Mark scheme Oct 2020 Paper 2 (Mechanics) Q3(b)
Oct 2020 · Paper 3 (Mechanics) · Q3
Mark scheme Oct 2020 Paper 3 (Mechanics) Q3(ii)
June 2019 · AS Paper 2 (Mechanics) · Q3
Mark scheme June 2019 Paper 2 (Mechanics) Q3(b)
June 2019 · Paper 3 (Mechanics) · Q1
Mark scheme June 2019 Paper 3 (Mechanics) Q1(b)
June 2018 · AS Paper 2 · Q8
Mark scheme June 2018 Paper 2 Q8(b)
June 2018 · Paper 3 · Q6
Mark scheme June 2018 Paper 3 Q6