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GCE MAY 2009 : AS, M1: Mechanics 1

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ADVANCED SUBSIDIARY (AS) General Certificate of Education 2009 Mathematics assessing Module M1: Mechanics 1 AMM11 Assessment Unit M1 [AMM11] FRIDAY 15 MAY, MORNING TIME 1 hour 30 minutes. INSTRUCTIONS TO CANDIDATES Write your Centre Number and Candidate Number on the Answer Booklet provided. Answer all eight questions. Show clearly the full development of your answers. Answers should be given to three significant figures unless otherwise stated. You are permitted to use a graphic or scientific calculator in this paper. INFORMATION FOR CANDIDATES The total mark for this paper is 75 Figures in brackets printed down the right-hand side of pages indicate the marks awarded to each question or part question. Answers should include diagrams where appropriate and marks may be awarded for them. Take g = 9.8 m s 2, unless specified otherwise. A copy of the Mathematical Formulae and Tables booklet is provided. 4358 Answer all eight questions. Show clearly the full development of your answers. Answers should be given to three significant figures unless otherwise stated. 1 Fig. 1 below shows a triangle ABC which is right angled at B. Angle BCA is 50 Forces of magnitudes 5 N, 8 N and 15 N, respectively, act along the sides AB, BC and CA of the triangle as shown. A 5 15 50 B 8 C Fig. 1 Find the magnitude and direction of the resultant of these forces. 2 [8] A uniform rod AB of mass 80 kg and length 10 m rests in equilibrium on two supports P and Q as shown in Fig. 2 below. AP = 2 m, QB = 3 m. 3 2 A P Q B Fig. 2 (i) Draw a diagram showing all the external forces acting on the rod. [2] (ii) Find the magnitudes of the reactions at P and Q. [6] An additional mass of M kg is placed at B. (iii) Find M if the rod is about to tilt. 4358 [4] 2 [Turn over 3 A stone is thrown vertically upwards from a point P with a speed of 14 m s 1 (i) Find the maximum height reached by the stone. (ii) Find the length of time for which the stone is more than 8.4 m above P. 4 [4] [5] A car of mass 800 kg pulls a trailer of mass 200 kg along a straight horizontal road, as shown in Fig. 3 below. The car and trailer have a constant acceleration of 2 m s 2 The driving force produced by the car s engine is 2400 N. The resistances acting on the car and trailer are 300 N and R newtons respectively. Fig. 3 (i) Draw a diagram showing all the external forces acting on the car and trailer. (ii) Find R, and the tension in the towbar between the car and the trailer. 5 [2] [7] A particle, A, of mass 0.4 kg is travelling along a smooth horizontal table with a speed of u m s 1 It collides directly with another particle, B, of mass 0.6 kg which is at rest. Following the collision, A is at rest. (i) Find, in terms of u, the speed of B immediately after the collision. (ii) Find, in terms of u, the impulse given by B to A. 4358 [4] [3] 3 [Turn over 6 Fig. 4 below shows a block of mass 10 kg being pulled up a rough plane inclined at 30 to the horizontal by a force of 100 N, acting parallel to the plane. The coefficient of friction between the block and the plane is 0.3 100 10 30 Fig. 4 (i) Draw a diagram showing all the external forces acting on the block. (ii) Find the acceleration of the block. 7 [2] [6] At time t seconds, t by 0, the velocity v m s 1 of a particle P moving in a straight line is given v = t2 5t + 6 (i) Find the times when the particle is instantaneously at rest. [3] (ii) Find an expression for the acceleration of P at time t. [2] (iii) Given that, at t = 6, P is moving through a fixed point O, find an expression for s, the displacement of P from O, at time t. [4] (iv) Hence find the distance travelled by P in the first 3 seconds of its motion. 8 [4] A motorcyclist is travelling along a straight horizontal motorway. At time t = 0 seconds the motorcyclist, who is travelling at a speed of 30 m s 1 and accelerating at 0.2 m s 2, passes a police car which is at rest. 5 seconds later the police car sets off in pursuit of the motorcyclist, accelerating at 1 m s 2 Find the time taken for the police car to draw level with the motorcyclist. [9] S 12/07 936-003-1 [Turn over

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Additional Info : Gce Mathematics May 2009 Assessment Unit M1 Module M1 : Mechanics 1
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