Constant Acceleration textbook practice

Question (1)

A car is travelling along a straight horizontal road with constant acceleration. The car passes over three consecutive points A, B and C where AB= 100 m and BC = 300 m. The speed of the car at B is 14ms-1 and the speed of the car at C is 20ms-1.

Find:

(a) the acceleration of the car

(b) b the time take for the car to travel from A to C.

Question (2)

A particle moves in a straight line from A to B with constant acceleration 1.5 ms-2. It then moves along the same straight line from B to C with a different acceleration. The speed of the particle at A is 1 ms-1 and the speed of the particle at C is 43ms-1. The particle takes 12s to move from A to B and 10s to move from B to C.

Find:

(a) the speed of the particle at B

(b) the acceleration of the particle as it moves from B to C

(c) the distance from A to C.

Solution for Question 1 and 2

Question (3)

A particle moves 451 m in a straight line. The diagram shows a speed-time graph illustrating the motion of the particle. The particle starts at rest and accelerates at a constant rate for 8 seconds reaching a speed of 2u ms^-1. The particle then travels at a constant speed for 12 seconds before decelerating uniformly, reaching a speed of u ms^-1 at time t = 26 s.

Find:

a) The value of u

b) The distance travelled by the particle while its speed is less than u ms^-1.

Solution for Question 3

Question (4)

A pebble is projected vertically upward with speed 21 ms^-1 from a point 32 m above the ground. Find:

a) The speed with which the pebble strikes the ground

b) The total time for which the pebble is more than 40 m above the ground.

c) Sketch a velocity-time graph for the motion of the pebble from the instant it is projected to the instant it hits the ground, showing the values of t at any points where the graph intercepts the horizontal axis.

Solution for Question 4

Question (5)

A particle is projected vertically upward with a speed of 30 ms^-1 from a point A. The point B is h metres above A. The particle moves freely under gravity and is above B for a time 2.4 s. Calculate the value of h.

Solution for Question 5

Question (6)

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 ms^-1. Car B passes O with a speed of 20 ms^-l, and has constant acceleration of 4 ms^-2. Find:

a) The speed of B when it has travelled 78 m from O

b) The distance from O of A when B is 78 m from O

c) The time when B overtakes A.

Solution for Question 6

Question (7)

A car is being driven on a straight stretch of motorway at a constant velocity of 34 ms^-1 when it passes a velocity restriction sign S warning of road works ahead and requiring speeds to be reduced to 22 ms^-1. The driver continues at her velocity for 2 s after passing S. She then reduces her velocity to 22 ms^-1 with constant deceleration of 3 ms^-2, and continues at the lower velocity.

a) Draw a velocity-time graph to illustrate the motion of the car after it passes S.

b) Find the shortest distance before the road works that S should be placed on the road to ensure that a car driven in this way has had its velocity reduced to 22 ms^-1 by the time it reaches the start of the road works.

Solution for Question 7

Question (8)

A train starts from rest at station A and accelerates uniformly at 3x ms^-2 until it reaches a velocity of 30 ms^-1. For the next T seconds the train maintains this constant velocity. The train then decelerates uniformly at x ms^-2 until it comes to rest at a station B. The distance between the stations is 6 km and the time taken from A to B is 5 minutes.

(a) Sketch a velocity-time graph to illustrate this journey.

(b) Show that 40/x + T = 300.

(c) Find the value of T and the value of x.

(d) Calculate the distance the train travels at constant velocity.

(e) Calculate the time taken from leaving A until reaching the point halfway between the stations.

Solution for Question 8