The language of kinematics and motion graphsAQA A-Level Maths: Subtopic test

1. 1
   A runner starts at point $O$ on a straight track and runs $40$ m in the positive direction in $8$ s. She then immediately turns round and runs $15$ m back towards $O$ in $5$ s.

   (a)

   Find the total distance travelled by the runner.

   [1 mark]

   • A$25$ m
   • B$40$ m
   • C$15$ m
   • D$55$ m

   (b)

   Find the average velocity of the runner over the whole $13$ s.

   [1 mark]

   • A$1.92$ m s$^{-1}$ in the positive direction
   • B$4.23$ m s$^{-1}$
   • C$3.08$ m s$^{-1}$
   • D$1.15$ m s$^{-1}$

   (c)

   Find the average speed of the runner over the whole $13$ s, and explain why it is different from the magnitude of her average velocity.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A train travels along a straight track. Its velocity-time graph is made of three straight-line sections: the velocity increases uniformly from $0$ to $20$ m s$^{-1}$ in $10$ s, then stays constant at $20$ m s$^{-1}$ for $30$ s, then decreases uniformly to $0$ in $20$ s.

   (a)

   Find the acceleration of the train during the first $10$ s.

   [1 mark]

   • A$0.5$ m s$^{-2}$
   • B$20$ m s$^{-2}$
   • C$2$ m s$^{-2}$
   • D$-1$ m s$^{-2}$

   (b)

   Find the total distance travelled by the train.

   [1 mark]

   • A$600$ m
   • B$900$ m
   • C$1200$ m
   • D$700$ m

   (c)

   Find the acceleration of the train in the last $20$ s, and state what the sign of your answer tells you.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A cyclist travels along a straight road. Her displacement $s$ metres from a point $O$, at time $t$ seconds, has a displacement-time graph made of three straight-line sections: $s$ increases uniformly from $0$ to $100$ when $t$ goes from $0$ to $20$; $s$ stays at $100$ from $t=20$ to $t=50$; and $s$ decreases uniformly from $100$ to $40$ from $t=50$ to $t=80$.

   (a)

   Find the velocity of the cyclist in each of the three stages of her journey.

   [3 marks]

   (b)

   Find, for the whole $80$ s, (i) the total distance travelled and the average speed, (ii) the average velocity.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A lift moves vertically from the ground floor, with upwards as the positive direction. Its velocity-time graph is made of three straight-line sections: the velocity increases uniformly from $0$ to $3$ m s$^{-1}$ in $4$ s, then is constant at $3$ m s$^{-1}$ for $10$ s, then decreases uniformly to $0$ in $3$ s.

   (a)

   (i) Find the acceleration of the lift in the first stage.
   (ii) Find the height reached by the lift when it stops.
   (iii) Find the average velocity over the whole journey.

   [6 marks]

   (b)

   After a pause of $5$ s at the top, the lift returns to the ground floor with a constant velocity of $-2.7$ m s$^{-1}$.
   (i) Find the time taken for the downward journey.
   (ii) Find the average speed for the whole round trip, including the pause.
   (iii) Explain why the average velocity for the whole round trip is zero but the average speed is not.

   [6 marks]

   Total for question 4: 12 marks

End of questions