Constant acceleration (suvat) equationsEdexcel A-Level Maths: Subtopic test

1. 1
   A ball is thrown vertically upwards from ground level with speed $14$ m s$^{-1}$. The ball is modelled as a particle moving freely under gravity, with $g=9.8$ m s$^{-2}$ and upwards taken as positive.

   (a)

   What is the greatest height reached by the ball?

   [1 mark]

   • A$10$ m
   • B$20$ m
   • C$1.43$ m
   • D$9.1$ m

   (b)

   How long is the ball in the air before it returns to ground level?

   [1 mark]

   • A$0.71$ s
   • B$5.71$ s
   • C$2.86$ s
   • D$1.43$ s

   (c)

   Find the speed of the ball 1.5 s after it is thrown, and state whether it is moving upwards or downwards.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A car brakes with constant deceleration from a speed of $30$ m s$^{-1}$ and comes to rest after travelling 90 m in a straight line.

   (a)

   What is the magnitude of the car's deceleration?

   [1 mark]

   • A$0.33$ m s$^{-2}$
   • B$5$ m s$^{-2}$
   • C$10$ m s$^{-2}$
   • D$2.5$ m s$^{-2}$

   (b)

   The car has travelled 40 m since it began to brake. What is its speed at that instant?

   [1 mark]

   • A$500$ m s$^{-1}$
   • B$36.1$ m s$^{-1}$
   • C$26.5$ m s$^{-1}$
   • D$22.4$ m s$^{-1}$

   (c)

   Find the distance the car travels in the first 2 s of braking.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A particle moves in a straight line with constant acceleration $a$ m s$^{-2}$. At $t=0$ its velocity is $u$ m s$^{-1}$. At time $t$ seconds its velocity is $v$ m s$^{-1}$ and its displacement from its starting point is $s$ metres.

   (a)

   Using the fact that the area under a velocity--time graph is the displacement, show that $s=ut+\frac12at^2$.

   [3 marks]

   (b)

   In one case $u=4$, $a=2$ and $s=21$. Find $v$ and $t$.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A speeding car $Q$ passes a point $A$ at a constant speed of $25$ m s$^{-1}$. At that instant a police car $P$, at rest at $A$, starts to move in the same direction with constant acceleration $4$ m s$^{-2}$. Time $t$ is measured in seconds from this instant.

   (a)

   (i) Write down expressions for the distances travelled by $Q$ and by $P$ after $t$ seconds.
   (ii) Find the time at which $P$ catches $Q$.
   (iii) Find the speed of $P$ at that instant.

   [6 marks]

   (b)

   Suppose instead that $P$ cannot exceed $40$ m s$^{-1}$, and travels at this constant speed once it reaches it. Find the time at which $P$ catches $Q$, and the distance from $A$ at which this happens.

   [6 marks]

   Total for question 4: 12 marks

End of questions