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Kinematics and Dynamics · CAPE Applied Mathematics Unit 2

42 past-paper questions on Kinematics and Dynamics, part of Module 3: Particle Mechanics, from every CAPE Applied Mathematics Unit 2 paper on Quelpr.

Practise Kinematics and Dynamics
  1. 5(a)(ii)3 marks· CAPE Applied Mathematics Unit 2 · 2008 (second paper) · Paper 2State the principle of conservation of linear momentum.
  2. 5(b)(ii)11 marks· CAPE Applied Mathematics Unit 2 · 2008 (second paper) · Paper 2Calculate the distance and the time required to bring the vehicle to rest by a braking force of 1000 N applied immediately after the impact.
  3. 5(a)(i)7 marks· CAPE Applied Mathematics Unit 2 · 2010 · Paper 2Calculate the acceleration of the particle.
  4. 5(a)(ii)8 marks· CAPE Applied Mathematics Unit 2 · 2010 · Paper 2Calculate the time taken to travel 105 metres from O.
  5. 5(b)(i)6 marks· CAPE Applied Mathematics Unit 2 · 2010 · Paper 2Calculate the acceleration.
  6. 5(b)(ii)4 marks· CAPE Applied Mathematics Unit 2 · 2010 · Paper 2Calculate the velocity of the particle at a distance of 50 metres from P.
  7. 5(a)(ii)a)4 marks· CAPE Applied Mathematics Unit 2 · 2011 · Paper 2Calculate the acceleration of the car.
  8. 5(a)(ii)b)5 marks· CAPE Applied Mathematics Unit 2 · 2011 · Paper 2Calculate the tractive force of the car.
  9. 5(b)(i)5 marks· CAPE Applied Mathematics Unit 2 · 2011 · Paper 2Determine the acceleration of motion.
  10. 5(b)(ii)3 marks· CAPE Applied Mathematics Unit 2 · 2011 · Paper 2Determine the tension in the string.
  11. 6(a)(i)4 marks· CAPE Applied Mathematics Unit 2 · 2011 · Paper 2Sketch a velocity-time graph for the motion of the train.
  12. 6(a)(ii)10 marks· CAPE Applied Mathematics Unit 2 · 2011 · Paper 2Using the graph, determine the initial uniform acceleration of the train, if the time taken for the whole journey is 6 minutes.
  13. 5(c)(i)7 marks· CAPE Applied Mathematics Unit 2 · 2013 · Paper 2Show that t = \frac{1}{k}\ln\left(\frac{10}{10 - kx}\right).
  14. 5(c)(ii)3 marks· CAPE Applied Mathematics Unit 2 · 2013 · Paper 2On reaching the top of the 75 m long hill, his velocity has dropped to 4\text{ ms}^{-1}. Find the value of k.
  15. 6(a)(i)3 marks· CAPE Applied Mathematics Unit 2 · 2013 · Paper 2Determine the acceleration, a\text{ ms}^{-2}, of the system.
  16. 6(a)(ii)2 marks· CAPE Applied Mathematics Unit 2 · 2013 · Paper 2Determine the tension, T\text{ N}, in the string.
  17. 6(a)(iii)3 marks· CAPE Applied Mathematics Unit 2 · 2013 · Paper 2Determine the distance travelled by EACH particle during the first 6 seconds.
  18. 6(b)4 marks· CAPE Applied Mathematics Unit 2 · 2013 · Paper 2A ball, of mass 1.5 kg, strikes a smooth vertical wall horizontally with a speed of 7\text{ ms}^{-1} and bounces off it at 5\text{ ms}^{-1}. Calculate the impulse of the ball.
  19. 5(a)(i)4 marks· CAPE Applied Mathematics Unit 2 · 2014 · Paper 2On the answer sheet provided as an insert, draw a displacement time graph for 0 ≤ t ≤ 8.
  20. 5(a)(ii)a)3 marks· CAPE Applied Mathematics Unit 2 · 2014 · Paper 2From your graph calculate the total distance travelled in the period 0 ≤ t ≤ 5.
  21. 5(a)(ii)b)3 marks· CAPE Applied Mathematics Unit 2 · 2014 · Paper 2From your graph calculate the average velocity over the period 0 ≤ t ≤ 5.
  22. 5(a)(ii)c)2 marks· CAPE Applied Mathematics Unit 2 · 2014 · Paper 2From your graph calculate the time at which the velocity is zero.
  23. 6(c)6 marks· CAPE Applied Mathematics Unit 2 · 2014 · Paper 2Find the value of T.
  24. 5(a)(ii)8 marks· CAPE Applied Mathematics Unit 2 · 2015 · Paper 2The particle is released from rest. Determine the tension, T, in the string and the acceleration, a, of the particle.
  25. 5(b)(i)2 marks· CAPE Applied Mathematics Unit 2 · 2015 · Paper 2Find in vector form the acceleration when t = 3.
  26. 5(b)(ii)4 marks· CAPE Applied Mathematics Unit 2 · 2015 · Paper 2Find in vector form the position of the particle when t = 3.
  27. 5(c)4 marks· CAPE Applied Mathematics Unit 2 · 2015 · Paper 2A particle of mass m falls vertically from rest through a medium with resistance to motion proportional to v, where v is its velocity at time t. Obtain a differential equation relating v and t.
  28. 6(a)3 marks· CAPE Applied Mathematics Unit 2 · 2015 · Paper 2A pressure washer hose delivers 10 kg of water per second horizontally, hitting a wall at a speed of 30 m s⁻¹. Assuming water does not bounce off, find the average force exerted on the wall.
  29. 6(b)6 marks· CAPE Applied Mathematics Unit 2 · 2015 · Paper 2A 5-tonne truck moving at 4 m s⁻¹ and a 3-tonne truck moving at 7 m s⁻¹ travel along the same road in opposite directions, collide, and couple together. Find the velocity and direction in which they continue to move.
  30. 6(d)4 marks· CAPE Applied Mathematics Unit 2 · 2015 · Paper 2A string passes over a fixed, smooth, weightless pulley, with masses of 3 kg and 5 kg attached to each end. Calculate the acceleration of the system.
  31. 5(b)(i)3 marks· CAPE Applied Mathematics Unit 2 · 2016 · Paper 2Draw a clearly labelled diagram showing all the forces acting on the system after the engine is shut off.
  32. 5(b)(ii)4 marks· CAPE Applied Mathematics Unit 2 · 2016 · Paper 2Determine the decelerating force acting on the system.
  33. 5(b)(iii)6 marks· CAPE Applied Mathematics Unit 2 · 2016 · Paper 2Determine the time taken to reduce speed from 80 km h⁻¹ to 44 km h⁻¹.
  34. 6(c)(i)4 marks· CAPE Applied Mathematics Unit 2 · 2016 · Paper 2Calculate the speed of vehicle B immediately after the collision.
  35. 6(c)(ii)1 mark· CAPE Applied Mathematics Unit 2 · 2016 · Paper 2State the direction of motion of vehicle B after the collision.
  36. 6(c)(iii)5 marks· CAPE Applied Mathematics Unit 2 · 2016 · Paper 2Calculate the time taken for vehicle A to come to rest after the collision.
  37. 5(a)(i)4 marks· CAPE Applied Mathematics Unit 2 · 2017 · Paper 2Draw a diagram to illustrate this information, showing the forces acting on the system.
  38. 5(a)(ii)6 marks· CAPE Applied Mathematics Unit 2 · 2017 · Paper 2Determine the masses of the particles, A and B.
  39. 5(a)(iii)2 marks· CAPE Applied Mathematics Unit 2 · 2017 · Paper 2Calculate the tension, T, in the string.
  40. 6(b)10 marks· CAPE Applied Mathematics Unit 2 · 2017 · Paper 2Calculate the velocities V_1 and V_2.
  41. 6(a)(i)9 marks· CAPE Applied Mathematics Unit 2 · 2018 · Paper 2Given that the impulse acting on T has magnitude 0.8 N, calculate the speed, v, and the loss of kinetic energy in the collision.
  42. 6(a)(ii)3 marks· CAPE Applied Mathematics Unit 2 · 2018 · Paper 2Particle T subsequently collides and coalesces with a stationary particle of mass 0.3 kg. Calculate the speed, v_c, of the combined particles after this collision.

Related topics in Module 3: Particle Mechanics