CAIE A-Level Mathematics 4.4 Newton's Laws of Motion Question Bank

CAIE A-Level Mathematics 4.4 Newton's Laws of Motion Question Bank
Cambridge International AS & A Level Mathematics 9709 syllabus for exams in 2028, 2029 and 20302028–2030

Practise applying Newton's second law to particles, vehicles and connected systems with weight, reaction, tension, thrust, resistance and friction on horizontal or inclined paths.

Exam points

  • draw and resolve the forces on each body before writing ΣF = ma along its motion
  • use a shared acceleration and appropriate tension relations for connected particles
  • solve a whole-system equation for acceleration, then an individual equation for tension or thrust

Covered syllabus points

4.4.1—Forces4.4.2—Mass and weight4.4.3—Constant acceleration4.4.4—Connected-particle models

Question 1(a)

[Maximum number: 2]

A car of mass 900 kg is moving along a straight horizontal road against a constant resistance to motion of 350 N . At an instant when the car is moving at 15 ms−115 \mathrm{~ms}^{-1} its acceleration is 0.25 ms−20.25 \mathrm{~ms}^{-2}.

Find the driving force of the car's engine at this instant.

Question 2

[Maximum number: 5]

A railway locomotive of mass 240000 kg is towing a coach of mass 36000 kg down a hill inclined at an angle of sin⁡−10.04\sin ^{-1} 0.04 to the horizontal. The driving force produced by the locomotive is 450000 N and there are resistances to motion of 120000 N on the locomotive and 15000 N on the coach. The coupling between the locomotive and the coach is light, rigid and parallel to the hill.

Find the acceleration of the locomotive and the tension in the coupling.

Question 5

[Maximum number: 8]

A straight slope of length 60 m is inclined at an angle of 12∘12^{\circ} to the horizontal. A bobsled starts at the top of the slope with a speed of 5 ms−15 \mathrm{~ms}^{-1}. The bobsled slides directly down the slope.

Question 5(a)

(a)

It is given that there is no resistance to the bobsled's motion.

Find its speed when it reaches the bottom of the slope.

[ 3 ]

Question 5(b)

(b)

It is given instead that the coefficient of friction between the bobsled and the slope is 0.03 .

Find the time that it takes for the bobsled to reach the bottom of the slope.

[ 5 ]