Mathematics 2024 · Oct/Nov

A block of mass 20 kg is held at rest at the top of a plane inclined at 30° to the horizontal. The block is projected with speed 5 m s down a line of greatest slope of the plane. There is a resistance force acting on the block. As the block moves 2 m down the plane from its point of projection, the work done against this resistance force is 50 J. Find the speed of the block when it has moved 2 m down the plane. [4] iTTTTuTTTTTTT i

A cyclist is riding along a straight horizontal road. The total mass of the cyclist and his bicycle is 90 kg. The power exerted by the cyclist is 250 W. At an instant when the cyclist' s speed is 5 m s , his acceleration is 0.1 m s

Find the value of the constant resistance to motion acting on the cyclist. [3] The cyclist comes to the bottom of a hill inclined at 2° to the horizontal.

Given that the power and resistance to motion are unchanged, find the steady speed which the cyclist could maintain when riding up the hill. [2] iTTTTuTTTTTTTdi 45° 0.2 kg 0.1 kgA B The diagram shows two particles, A and B, of masses 0.2 kg and 0.1 kg respectively. The particles are suspended below a horizontal ceiling by two strings, AP and BQ, attached to fixed points P and Q on the ceiling. The particles are connected by a horizontal string, AB. Angle °APQ 45= and °PBQ i=. Each string is light and inextensible. The particles are in equilibrium.

Find the value of the tension in the string AB. [2] iTTTTuTTTTTTToi

Find the value of i and the tension in the string BQ. [4] iTTTTuTTTTTTTci

Two particles, P and Q, of masses 2m kg and m kg respectively, are held at rest in the same vertical line. The heights of P and Q above horizontal ground are 1 m and 2 m respectively. P is projected vertically upwards with speed 2 m s . At the same instant, Q is released from rest.

Find the speed of each particle immediately before they collide. [4] iTTTTuTTTTTTTui

It is given that immediately after the collision the downward speed of Q is 3.5 m s Find the speed of P at the instant that it reaches the ground. [5] iTTTTuTTTTTTTmi

A particle, P, travels in a straight line, starting from a point O with velocity 6 m s . The acceleration of P at time t s after leaving O is a m s , where .at15 =- for t01GG, .at t153 for t12.

Find the velocity of P at t1=.

Given that there is no change in the velocity of P when t1=, find an expression for the velocity of P for t12. [3] iTTTTuTTTTTThTi

Given that the velocity of P is positive for t4G, find the total distance travelled between t0= and t4=. [4] iTTTTuTTTTTThhi 0.25 m 0.3 kg 0.2 kg Two particles, A and B, of masses 0.2 kg and 0.3 kg respectively, are attached to the ends of a light inextensible string. The string passes over a small fixed smooth pulley which is attached to the bottom of a rough plane inclined at an angle i to the horizontal where .sin0 6i= . Particle A lies on the plane, and particle B hangs vertically below the pulley , 0.25 m above horizontal ground. The string between A and the pulley is parallel to a line of greatest slope of the plane (see diagram). The coefficient of friction between A and the plane is 1.125 . Particle A is released from rest.

Find the tension in the string and the magnitude of the acceleration of the particles. [7] iTTTTuTTTTTThii

When B reaches the ground, it comes to rest. Find the total distance that A travels down the plane from when it is released until it comes to rest. You may assume that A does not reach the pulley . [4] iTTTTuTTTTTThsi Additional page If you use the following page to complete the answer to any question, the question number must be clearly shown. iTTTTuTTTTTTh i BLANK PAGE * 0000800000015 * iTTTTuTTTTTThdi Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable ef fort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge Assessment International Education Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. Local Examinations Syndicate (UCLES), which is a department of the University of Cambridge. BLANK PAGE * 0000800000016 * iTTTTuTTTTTThoi