Exam-Style Problems
⬅ Back to SubchapterMay/June 2026 p42 q1
A car of mass \(960\text{ kg}\) is moving on a straight horizontal road. There is a constant force of magnitude \(620\text{ N}\) resisting the motion of the car.
(a) Calculate the power developed by the engine of the car when it is moving at a constant speed of \(25\text{ m s}^{-1}\).
(b) Given that the power is suddenly increased by \(12\text{ kW}\), find the instantaneous acceleration of the car.
May/June 2026 p42 q2
Two particles, \(A\) and \(B\), of masses \(2.5\text{ kg}\) and \(3.5\text{ kg}\) respectively are at rest on a straight smooth horizontal track. Particle \(B\) is situated \(9\text{ m}\) from a vertical wall which is fixed at right angles to the track.
Particle \(A\) is projected directly towards \(B\) with a speed of \(3\text{ m s}^{-1}\). In the subsequent motion, \(A\) collides and coalesces with \(B\) to form particle \(C\). Particle \(C\) then collides directly with the wall and rebounds. The collision of \(C\) with the wall reduces the speed of \(C\) by \(25\%\).
(a) Find the speed of \(C\) after it rebounds from the wall.
(b) Hence find the time from the instant at which \(A\) and \(B\) collide until \(C\) is once again a distance of \(9\text{ m}\) from the wall.
May/June 2026 p42 q3
Two particles, \(A\) and \(B\), of masses \(0.5\text{ kg}\) and \(0.8\text{ kg}\) respectively are attached to the ends of a light inextensible string. The string passes over a small smooth pulley fixed at the end of a rough horizontal plane and to the top of a smooth inclined plane. Particle \(A\) is held on the horizontal plane, while \(B\) lies on the inclined plane, which makes an angle of \(55^\circ\) with the horizontal. The string is in the same vertical plane as a line of greatest slope of the inclined plane (see diagram).
Particle \(A\) is released from rest with the string taut. Particle \(B\) moves \(0.3\text{ m}\) down the inclined plane in \(0.4\text{ s}\).
(a) Find the tension in the string.
(b) Find the coefficient of friction between \(A\) and the horizontal plane.
(c) After \(B\) has been moving for \(0.4\text{ s}\), the string suddenly breaks. Given that \(A\) subsequently comes to rest on the horizontal plane, find the work done by the frictional force in bringing \(A\) to rest.
You may assume that \(A\) does not reach the pulley.
May/June 2026 p42 q4
A particle \(P\) is projected from a point \(A\) with speed \(4\text{ m s}^{-1}\) up a line of greatest slope of a rough plane inclined at an angle \(\theta\) to the horizontal, where \(\tan\theta=\frac43\).
\(P\) comes to instantaneous rest at a point \(B\) on the plane (see diagram).
The coefficient of friction between \(P\) and the plane is \(\frac13\).
(a) Using an energy method, show that the distance \(AB\) is \(0.8\text{ m}\).
(b) After coming to instantaneous rest at \(B\), the particle slides down the plane.
Find the total time from the instant at which \(P\) is projected from \(A\) until it returns to \(A\).
May/June 2026 p42 q5
The points \(A\) and \(B\) are at the same vertical height \(h\text{ m}\) above horizontal ground. A particle \(P\) is released from rest from \(A\). One second later, a particle \(Q\) is projected vertically downwards from \(B\) with speed \(18\text{ m s}^{-1}\).
Given that \(P\) and \(Q\) reach the ground at the same time, find the value of \(h\).