CAIE Mathematics (9709)

A crate is being pushed in a straight line along a horizontal surface by a force of magnitude 25 N inclined at 20° above the horizontal. The crate moves a distance of 12 m in 8 seconds with constant speed.

Find the constant speed of the crate.

Find the work done by the 25 N force.

Find the power at which the 25 N force is working. [1] bTTTTuTTTTTTTsb

Two particles P and Q, of masses 0.2 kg and 0.1 kg respectively, are free to move in a straight line on a smooth horizontal plane. P is projected towards Q with speed .ms5 At the same instant, Q is projected away from P with speed .ms2 When P collides with Q, the particles coalesce. Find the kinetic ener gy lost during the collision. [4] bTTTTuTTTTTTT b 2.4 m 2.6 m 35 N A particle P of mass m kg is attached to one end of a light inextensible string of length 2.6 m. The other end of the string is attached to a fixed point on a horizontal ceiling, and the string is taut. The particle is held in equilibrium by a force of magnitude 35 N, acting in a vertical plane which is perpendicular to the ceiling and contains the string. The force acts in a direction perpendicular to the string (see Find, in either order , the value of m and the value of T. [4] bTTTTuTTTTTTTdb

A car is travelling along a straight horizontal road. The car passes through a point A, on the road travelling at a speed of ms15 , and then accelerates uniformly at .ms04 for 30 seconds. The car then moves at constant speed for 3T seconds, where T301. The car then decelerates uniformly at .ms02 and after a further T seconds passes through a point B on the road.

On the given axes, sketch a velocity-time graph for the motion of the car between points A and B. [2] v (m s t

The distance from A to B is 2750 m.

Find the value of T. [6] bTTTTuTTTTTTTob The car continues its journey from B, decelerating uniformly at .ms05 until it comes to rest at a point C on the road.

Find the total distance from A to C. [3] bTTTTuTTTTTTTcb 5 kg 4 kg 3 kg30° One end of a light inextensible string is attached to a particle A of mass 3 kg. The other end of the string is attached to a particle B of mass 4 kg. Particle A is in contact with a rough plane inclined at 30° to the horizontal, and particle B is in contact with a smooth horizontal plane. A second light inextensible string is attached to B. The other end of this second string is attached to a particle C of mass 5 kg which hangs vertically. Both strings are taut and pass over small smooth pulleys that are fixed at the ends of the horizontal plane. The part of the string from A to the pulley is parallel to a line of greatest slope of the inclined plane, and A, B and C are in the same vertical plane (see diagram). The system is released from rest. In the subsequent motion, C moves vertically downwards with acceleration ms2 , and neither A nor B reach a pulley .

Find the tensions in each of the strings. [3] bTTTTuTTTTTTTub

Find the coefficient of friction between A and the inclined plane. [4] When the system has been in motion for 1.5 s, the string attached to A breaks.

Find the total distance that A travels up the plane from the instant that the system is released from rest to the instant that A comes to instantaneous rest. [5] bTTTTuTTTTTTTmb

A particle P moves in a straight line and passes through the point A at time t0=. The velocity msv of P at time t seconds is given by ()vt t21 2 =+ -, where t03GG.

Find the maximum velocity of P in the interval t03GG. [5] bTTTTuTTTTTThTb It is given that in the interval t03GG the velocity of P is always positive.

Find the distance of P from A at the instant when P is moving at this maximum velocity . [4] bTTTTuTTTTTThhb

A particle P of mass 3 kg is projected with a speed of ms8 up a line of greatest slope of a rough plane inclined at 30° to the horizontal. P is projected from a point A on the plane and comes to instantaneous rest at a point B on the plane. P then slides back down the plane. The coefficient of friction between P and the plane is 3 Using an energy method throughout, find the speed of P at the instant it returns to A. [6] bTTTTuTTTTTThib Additional page If you use the following page to complete the answer to any question, the question number must be clearly shown. bTTTTuTTTTTThsb BLANK PAGE * 0000800000014 * bTTTTuTTTTTTh b BLANK PAGE * 0000800000015 * bTTTTuTTTTTThdb 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 * bTTTTuTTTTTThob