Constant acceleration formulaeEdexcel International A Level Maths: Subtopic test

1. 1
   A cyclist moves along a straight horizontal road. At the instant she passes a point $A$ her speed is $4$ m s⁻¹. She then accelerates uniformly at $0.5$ m s⁻² for $12$ s.

   (a)

   Find the speed of the cyclist after the $12$ s.

   [1 mark]

   • A$6$ m s⁻¹
   • B$10$ m s⁻¹
   • C$16.5$ m s⁻¹
   • D$7$ m s⁻¹

   (b)

   Find the distance the cyclist travels in the $12$ s.

   [1 mark]

   • A$120$ m
   • B$48$ m
   • C$36$ m
   • D$84$ m

   (c)

   Find the distance the cyclist travels in the last $2$ s of this motion.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A ball is thrown vertically upwards with speed $14$ m s⁻¹ from a point $2$ m above horizontal ground. Model the ball as a particle moving freely under gravity, and take $g=9.8$ m s⁻².

   (a)

   Find the greatest height of the ball above the ground.

   [1 mark]

   • A$12$ m
   • B$10$ m
   • C$22$ m
   • D$16$ m

   (b)

   Find the time taken for the ball to reach its highest point.

   [1 mark]

   • A$0.714$ s
   • B$2.86$ s
   • C$1.43$ s
   • D$1.56$ s

   (c)

   Find the speed of the ball when it hits the ground.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A train moves in a straight line from rest at station $P$ to rest at station $Q$. It accelerates uniformly at $0.5$ m s⁻² for $40$ s, then travels at constant speed for $150$ s, and finally decelerates uniformly at $0.8$ m s⁻² to rest at $Q$.

   (a)

   Find the distance travelled by the train while it is decelerating.

   [3 marks]

   (b)

   Find the total distance from $P$ to $Q$.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A police car $P$ is at rest at a point $O$ on a straight horizontal road. At the instant a speeding car $S$ passes $O$ with constant speed $30$ m s⁻¹, $P$ sets off in the same direction with constant acceleration $2.5$ m s⁻² until it reaches a speed of $40$ m s⁻¹, which it then maintains. Model both cars as particles.

   (a)

   Find the time, measured from the instant $S$ passes $O$, at which $P$ overtakes $S$.

   [6 marks]

   (b)

   Find the greatest distance between $P$ and $S$ before $P$ overtakes $S$.

   [6 marks]

   Total for question 4: 12 marks

End of questions