Language of kinematics and motion graphsEdexcel A-Level Maths: Subtopic test

1. 1
   A runner jogs 300 m east from a point $O$ in 100 s, then turns and jogs 100 m west in 50 s, all in a straight line. Take east as the positive direction.

   (a)

   What is the runner's displacement from $O$ at the end of the run?

   [1 mark]

   • A$400$ m east
   • B$100$ m east
   • C$200$ m east
   • D$300$ m east

   (b)

   What is the runner's average velocity for the whole run?

   [1 mark]

   • A$2.67$ m s$^{-1}$ east
   • B$0.67$ m s$^{-1}$ east
   • C$0.5$ m s$^{-1}$ east
   • D$1.33$ m s$^{-1}$ east

   (c)

   Find the average speed for the whole run, and explain why it is not equal to the magnitude of the average velocity.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A train moves along a straight track. Its velocity increases uniformly from $0$ to $20$ m s$^{-1}$ in 10 s, stays constant at $20$ m s$^{-1}$ for 30 s, then decreases uniformly to rest in 20 s. Consider its velocity--time graph.

   (a)

   What is the acceleration of the train during the final 20 s?

   [1 mark]

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

   (b)

   What is the total distance travelled by the train?

   [1 mark]

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

   (c)

   Find the average speed of the train over the whole journey.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A particle $P$ moves on a straight line through a fixed point $O$. Its displacement from $O$ is $s$ metres at time $t$ seconds. At $t=0$, $s=2$. From $t=0$ to $t=4$, $P$ moves with constant velocity to $s=14$. From $t=4$ to $t=7$, $P$ is at rest. From $t=7$ to $t=12$, $P$ moves with constant velocity to $s=-6$.

   (a)

   Find the velocity of $P$ in each of the three stages of its motion.

   [3 marks]

   (b)

   Find the total distance travelled by $P$ in the 12 s, the average speed over the 12 s, and the time at which $P$ passes through $O$.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A car travels along a straight road. At $t=0$ it passes a point $A$ at $8$ m s$^{-1}$ and accelerates uniformly for 6 s to $20$ m s$^{-1}$. It then travels at a constant $20$ m s$^{-1}$ for $T$ seconds, and finally decelerates uniformly to rest in 8 s. The total distance travelled from $A$ is 404 m.

   (a)

   (i) Find the acceleration in the first 6 s.
   (ii) Find the distance travelled in the first 6 s.
   (iii) Find the magnitude of the deceleration in the final 8 s.

   [6 marks]

   (b)

   (i) Find $T$.
   (ii) Find the average speed of the car for the whole journey.
   (iii) Explain why the average speed is less than $20$ m s$^{-1}$.

   [6 marks]

   Total for question 4: 12 marks

End of questions