CAIE A-Level Mathematics 4.3 Momentum Question Bank

CAIE A-Level Mathematics 4.3 Momentum Question Bank
Cambridge International AS & A Level Mathematics 9709 syllabus for exams in 2028, 2029 and 20302028–2030

Practise one-dimensional collisions by assigning signed velocities, conserving linear momentum and comparing kinetic energy before and after coalescence, rebound or separation.

Exam points

  • choose one positive direction and write every before- and after-impact velocity with a sign
  • apply total momentum before = total momentum after with the correct masses
  • calculate kinetic-energy loss only after solving all required post-impact speeds

Covered syllabus points

4.3.1—Momentum4.3.2—Momentum

Question 2(a)

[Maximum number: 3]

Two particles, P and Q, of masses 3 kg and 5 kg respectively, are at rest on a smooth horizontal plane. P is projected at a speed of 4 ms−14 \mathrm{~ms}^{-1} directly towards Q. After P and Q collide, P has speed 1 ms−11 \mathrm{~ms}^{-1}.

Find the two possible speeds of Q after the collision.

Question 5

[Maximum number: 7]

When a particle P of mass m kgm \mathrm{~kg} has speed u m s−1u \mathrm{~m} \mathrm{~s}^{-1}, its momentum is 4 Ns and its kinetic energy is 16 J.

Question 5(a)

(a)

Find the value of m and the value of u.

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Question 5(b)

(b)

P is now projected on a smooth horizontal surface with speed v ms^-1 directly towards a particle Q of mass 1.25 kg which is stationary. After P and Q collide, the velocity of P is w ms^-1 and the velocity of Q is 2 w m s^-1. The loss of kinetic energy in the collision is 25 J.

Find the value of v and the value of w.

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