deceleration = tan β = 30/6 = 5 m s-2 = 5(10) + ½ (5)(20) + (9)(30) + ½ (6)(30) = 50 + 50 + 270 + 90 = 460 m speed = total distance/total time = 460/20 = 23 m s-1 2005 OL A particle travels from p to q in a straight line. It starts from rest at p and accelerates uniformly to its maximum speed of 20 m/s in 10 seconds. The particle maintains this speed of 20 m/s for 15 seconds before decelerating uniformly to rest at q in a further 20 seconds. Draw a speed-time graph of the motion of the particle from p to q. Find the uniform acceleration of the particle. the uniform deceleration of the particle. pq, the distance from p to q. Find the average speed of the particle as it moves from p to q, giving your answer in the form a/b where a, b ∈ N. 2012 OL A car travels along a straight level road. It passes a P with a speed of 8 m s−1 and accelerates uniformly for 12 seconds to a speed of 32 m s−1. It then travels at a constant speed of 32 m s−1 for 7 seconds. Finally the car decelerates uniformly from 32 m s−1 to rest at a point Q. The car travels 128 metres while decelerating. Find (i) the acceleration (ii) the deceleration (iii) |PQ|, the distance from P to Q (iv) the speed of the car when it is 72 m from Q. 2010 OL A car travels a straight level road. It passes a point P at a speed of 12 m s-1 and accelerates uniformly for 6 seconds to a speed of 30 m s-1. It then travels at a constant speed of 30 m s-1 for 15 seconds. Finally the car decelerates uniformly from 30 m s-1 to rest at a point Q. The car travels 45 metres while decelerating. Find the acceleration the deceleration the distance from P to Q average speed of the car as it travels from P to Q 2006 OL A car travels along a straight level road. It passes a point p at a speed of 10 m/s and accelerates uniformly for 5 seconds to a speed of 30 m/s.
2003 (a) The points p, q and r all lie in a straight line. A passes point p with speed u m/s. The train is travelling with uniform retardation f m/s2. The train takes 10 seconds to travel from p to q and 15 seconds to travel from q to r, where | pq| = | qr | = 125 metres. Show that f = The train comes to rest s metres after passing r. Find s, giving your answer correct to the nearest metre. 2002 (b) difficult this until sixth year A particle, with initial speed u, moves in a straight line with constant acceleration. During the time interval from 0 to t, the particle travels a distance p. During the time interval from t to 2t, the particle travels a distance q. During the time interval from 2t to 3t, the particle travels a distance r. Show that 2q = p + r. Show that the particle travels a further distance 2r − q in the time interval from 3t to 4t. Slight Variations These seem tricky, but the procedure is your friend; pick two stages which have the same two unknowns and solve. 2007 (a) A particle is projected vertically downwards from the top of a tower with speed u m/s. It takes the particle 4 seconds to reach the bottom of the tower. During the third second of its motion the particle travels 29.9 metres. Find the value of u the height of the tower. 2011 (a) A particle is released from rest at A and falls vertically passing two points B and C. It reaches B t seconds and takes seconds to fall from B to C, a distance of 2.45 m. Find the value of t. 1986 (b) – just set up equations in Fifth year A particle starting from rest at p moves in a straight line to q with uniform acceleration. In the first second it travels 5 m. In the last three seconds of its motion before reaching q it travels of |pq|. Find the time in seconds from p to q. 2010 (b) - just set up equations in Fifth Year A particle passes P with speed 20 ms-1 and moves in a straight line to Q with uniform acceleration. In the first second of its motion after passing P it travels 25 m. In the last 3 seconds of its motion before reaching Q it travels of PQ. Find the distance from P to Q. Leave the questions below until Sixth Year