Acceleration and M1 A1
M1 SUVAT Equations
1. An aircraft moves along a straight horizontal runway with constant acceleration. It passes a point A on the runway with speed 16 m s–1. It then passes the point B on the runway with speed 34 m s–1. The distance from A to B is 150 m.
(a) Find the acceleration of the aircraft.
(3)
(b) Find the time taken by the aircraft in moving from A to B.
(2)
(c) Find, to 3 significant figures, the speed of the aircraft when it passes the point mid-way between A and B.
(2)
(Total 7 marks) 2. Three posts P, Q and R, are fixed in that order at the side of a straight horizontal road. The distance from P to Q is 45 m and the distance from Q to R is 120 m. A car is moving along the road with constant acceleration a m s–2. The speed of the car, as it passes P, is u m s–1. The car passes Q two seconds after passing P, and the car passes R four seconds after passing Q. Find
(i) the value of u,
(ii) the value of a.
(Total 7 marks)
3. A train moves along a straight track with constant acceleration. Three telegraph poles are set at equal intervals beside the track at points A, B and C, where AB = 50 m and BC = 50 m. The front of the train passes A with speed 22.5 m s–1, and 2 s later it passes B. Find
(a) the acceleration of the train,
(3)
(b) the speed of the front of the train when it passes C,
(3)
(c) the time that elapses from the instant the front of the train passes B to the instant it passes C.
(4)
(Total 10 marks)
4. Two cars A and B are moving in the same direction along a straight horizontal road. At time t = 0, they are side by side, passing a point O on the road. Car A travels at a constant speed of 30 m s–1. Car B passes O with a speed of 20 m s–1, and has constant acceleration of 4 m s–2. Find
(a) the speed of B when it has travelled 78 m from O,
(2)
(b) the distance from O of A when B is 78 m from O,
(4)
(c) the time when B overtakes A.
(5)(Total 11 marks)
Answers
5. (a) 342 = 162 + 2 . a . 150 M1 A1 Þ a = 3 m
1. An aircraft moves along a straight horizontal runway with constant acceleration. It passes a point A on the runway with speed 16 m s–1. It then passes the point B on the runway with speed 34 m s–1. The distance from A to B is 150 m.
(a) Find the acceleration of the aircraft.
(3)
(b) Find the time taken by the aircraft in moving from A to B.
(2)
(c) Find, to 3 significant figures, the speed of the aircraft when it passes the point mid-way between A and B.
(2)
(Total 7 marks) 2. Three posts P, Q and R, are fixed in that order at the side of a straight horizontal road. The distance from P to Q is 45 m and the distance from Q to R is 120 m. A car is moving along the road with constant acceleration a m s–2. The speed of the car, as it passes P, is u m s–1. The car passes Q two seconds after passing P, and the car passes R four seconds after passing Q. Find
(i) the value of u,
(ii) the value of a.
(Total 7 marks)
3. A train moves along a straight track with constant acceleration. Three telegraph poles are set at equal intervals beside the track at points A, B and C, where AB = 50 m and BC = 50 m. The front of the train passes A with speed 22.5 m s–1, and 2 s later it passes B. Find
(a) the acceleration of the train,
(3)
(b) the speed of the front of the train when it passes C,
(3)
(c) the time that elapses from the instant the front of the train passes B to the instant it passes C.
(4)
(Total 10 marks)
4. Two cars A and B are moving in the same direction along a straight horizontal road. At time t = 0, they are side by side, passing a point O on the road. Car A travels at a constant speed of 30 m s–1. Car B passes O with a speed of 20 m s–1, and has constant acceleration of 4 m s–2. Find
(a) the speed of B when it has travelled 78 m from O,
(2)
(b) the distance from O of A when B is 78 m from O,
(4)
(c) the time when B overtakes A.
(5)(Total 11 marks)
Answers
5. (a) 342 = 162 + 2 . a . 150 M1 A1 Þ a = 3 m