Kinematics (AS)AQA A-Level Maths: Topic test

1. 1
   A skier of mass $72$ kg slides down a straight slope. The resultant force on the skier down the slope is $108$ N. Take $g=9.8$ m s⁻².

   (a)

   Which of the following gives the newton in terms of SI base units?

   [1 mark]

   • Akg m² s⁻²
   • Bkg m s⁻¹
   • Ckg m⁻¹ s⁻²
   • Dkg m s⁻²

   (b)

   What is the acceleration of the skier down the slope?

   [1 mark]

   • A$0.67$ m s⁻²
   • B$7776$ m s⁻²
   • C$1.5$ m s⁻²
   • D$36$ m s⁻²

   (c)

   Calculate the weight of the skier, stating its unit.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A tram travels along a straight track. Its velocity increases uniformly from $0$ to $10$ m s⁻¹ in the first $5$ s, stays constant at $10$ m s⁻¹ for the next $20$ s, then decreases uniformly to $0$ in the final $10$ s.

   (a)

   What is the acceleration of the tram during the first $5$ s?

   [1 mark]

   • A$2$ m s⁻²
   • B$0.5$ m s⁻²
   • C$10$ m s⁻²
   • D$50$ m s⁻²

   (b)

   What is the total distance travelled by the tram?

   [1 mark]

   • A$250$ m
   • B$275$ m
   • C$350$ m
   • D$550$ m

   (c)

   Find the average speed of the tram for the whole journey.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A car travelling at $25$ m s⁻¹ along a straight road brakes with constant deceleration and comes to rest after travelling $62.5$ m.

   (a)

   Find the deceleration of the car.

   [3 marks]

   (b)

   A driver sees a hazard and takes $0.8$ s to react, during which the car continues at $25$ m s⁻¹, before braking as above. Find the total distance travelled and the total time from seeing the hazard to stopping.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A particle $P$ moves in a straight line. At time $t$ seconds, $t\ge0$, its velocity is $v=3t^2-18t+24$ m s⁻¹. At $t=0$, $P$ is at a fixed point $O$ on the line.

   (a)

   Find the times at which $P$ is instantaneously at rest and the acceleration of $P$ at each of these times. Explain what happens to the direction of motion of $P$ at the first of these times.

   [6 marks]

   (b)

   A second particle $Q$ starts from rest at $O$ at $t=0$ and moves along the same line with constant acceleration $4$ m s⁻². Find all the times when $P$ and $Q$ are at the same point.

   [6 marks]

   Total for question 4: 12 marks

5. 5
   A van of mass $1.2$ tonnes (where $1$ tonne $=1000$ kg) is travelling along a straight road at $90$ km h⁻¹. A constant resultant force of $3000$ N then acts on the van in its direction of motion.

   (a)

   What is the initial speed of the van in m s⁻¹?

   [1 mark]

   • A$90$
   • B$25$
   • C$324$
   • D$1.5$

   (b)

   What is the acceleration of the van?

   [1 mark]

   • A$2.5$ m s⁻²
   • B$0.4$ m s⁻²
   • C$25$ m s⁻²
   • D$3600$ m s⁻²

   (c)

   Find the time taken for the speed of the van to reach $126$ km h⁻¹.

   [2 marks]

   Total for question 5: 4 marks

6. 6
   A robot moves along a straight corridor. Its displacement $s$ metres from its starting point at time $t$ seconds is described by a graph made up of three straight lines: $s$ increases uniformly from $0$ to $12$ between $t=0$ and $t=6$; $s$ stays at $12$ between $t=6$ and $t=10$; and $s$ decreases uniformly from $12$ to $2$ between $t=10$ and $t=15$.

   (a)

   What is the velocity of the robot at $t=3$?

   [1 mark]

   • A$12$ m s⁻¹
   • B$0.5$ m s⁻¹
   • C$2$ m s⁻¹
   • D$4$ m s⁻¹

   (b)

   What is the total distance travelled by the robot in the $15$ seconds?

   [1 mark]

   • A$2$ m
   • B$12$ m
   • C$24$ m
   • D$22$ m

   (c)

   Find the average velocity of the robot over the $15$ seconds.

   [2 marks]

   Total for question 6: 4 marks

7. 7
   A ball is thrown vertically upwards from a point $2$ m above horizontal ground with speed $14$ m s⁻¹. Take $g=9.8$ m s⁻² and ignore air resistance.

   (a)

   Find the greatest height of the ball above the ground.

   [3 marks]

   (b)

   Find the time taken for the ball to reach the ground.

   [4 marks]

   Total for question 7: 7 marks

8. 8
   A model rocket is launched vertically from the ground at $t=0$, starting from rest. For $0\le t\le4$ (where $t$ is in seconds) its net upward acceleration is $(8-2t)$ m s⁻². At $t=4$ the engine cuts out and the rocket then moves freely under gravity, with $g=9.8$ m s⁻².

   (a)

   Find the velocity and the height of the rocket at $t=4$.

   [6 marks]

   (b)

   (i) Find the further height gained by the rocket after the engine cuts out. (ii) Find the greatest height of the rocket above the ground. (iii) Find the time for which the rocket continues to rise after the engine cuts out. (iv) State one modelling assumption.

   [6 marks]

   Total for question 8: 12 marks

End of questions