Constant acceleration past paper practice

Question 1:

Two small children, Ajaz and Beth, are running a 100 m race along a straight horizontal track. They both start from rest, leaving the start line at the same time.

Ajaz accelerates at 0.8ms^-2 up to a speed of 4 ms^-1 and then maintains this speed until he crosses the finish line.

Beth accelerates at 1 ms^-2 for T seconds and then maintains a constant speed until she crosses the finish line. Ajaz and Beth cross the finish line at the same time.

(a) Sketch, on the same axes, a speed-time graph for each child, from the instant when they leave the start line to the instant when they cross the finish line.

(b) Find the time taken by Ajaz to complete the race.

(c) Find the value of T

(d) Find the difference in the speeds of the two children as they cross the finish line.

(13 marks)

(June 2022, Q#7)

Solution for Question 1

Question 2:

A train travels for a total of 270 s along a straight horizontal track between two stations A and B. The train starts from rest at A and moves with constant acceleration for 60 s until it reaches a speed of V ms^-1. The train then travels at this constant speed V ms^-1 before it moves with constant deceleration for 30 s, coming to rest at B.

(a) Sketch below a speed-time graph for the journey of the train between the two stations A and B.

Given that the distance between the two stations is 4.5 km,

(b) Find the value of V,

(c) Find how long it takes the train to travel from station A to the point that is exactly halfway between the two stations.

The train is travelling at speed (1/4) V ms^-1 at times T₁ seconds and T₂ seconds after leaving station A.

(d) Find the value of T₁ and the value of T₂

(14 marks)

(January 2019, Q#6)

Solution for Question 2

Question 3:

A small ball is released from rest from a point that is 40 m above horizontal ground. The ball bounces on the ground and rebounds vertically. Each time the ball bounces on the ground, the speed of the ball is instantaneously reduced by 50%. The ball is modelled as a particle moving freely under gravity, from the instant when it is released until it first hits the ground, and between each successive bounce.

(a) Find the time from the instant when the ball is released from rest to the instant when it hits the ground for the second time.

(b) Find the maximum height reached by the ball above the ground after the ball's third bounce.

(9 marks)

(October 2019, Q#2)

Solution for Question 3