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 f m/s2. retardation 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 tricky, but the procedure is your friend; pick two stages which have the same two seem unknowns and solve. 2007 (a) A particle is projected vertically downwards from the top of a tower with speed m/s. u 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 and falls vertically passing two points and A B C. It reaches seconds and takes seconds to fall from to a distance of 2.45 m. B t B C, Find the value of t. 1986 (b) just set up equations in Fifth year – A particle starting from rest at moves in a straight line to with uniform acceleration. p q In the first second it travels 5 m. In the last three seconds of its motion before reaching it travels of |pq|. q Find the time in seconds from to p q. 2010 (b) - just set up equations in Fifth Year A particle passes with speed 20 ms-1 and moves in a straight line to with uniform acceleration. P Q In the first second of its motion after passing it travels 25 m. P In the last 3 seconds of its motion before reaching it travels of PQ. Q Find the distance from to P Q. Leave the questions below until Sixth Year
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
1.%20Linear%20Acceleration.docx