Motion graphsEdexcel International A Level Maths: Subtopic test

1. 1
   A sprinter's motion along a straight track is modelled by a velocity–time graph made of three straight-line sections. From t = 0 to t = 4 s, the velocity increases uniformly from 0 to 12 m s⁻¹. From t = 4 s to t = 10 s the velocity is constant at 12 m s⁻¹. From t = 10 s to t = 16 s the velocity decreases uniformly from 12 m s⁻¹ to 0.

   (a)

   What is the acceleration of the sprinter during the first 4 s?

   [1 mark]

   • A3 m s⁻²
   • B48 m s⁻²
   • C0.33 m s⁻²
   • D12 m s⁻²

   (b)

   What is the total distance travelled by the sprinter in the 16 s?

   [1 mark]

   • A96 m
   • B192 m
   • C132 m
   • D108 m

   (c)

   Find the average speed of the sprinter over the 16 s.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A cyclist rides along a straight road. Her displacement–time graph from the start point consists of three straight-line sections: from t = 0 to t = 5 s the displacement increases uniformly from 0 to 20 m; from t = 5 s to t = 8 s the displacement stays at 20 m; from t = 8 s to t = 14 s the displacement decreases uniformly from 20 m to 0.

   (a)

   What is the velocity of the cyclist during the first 5 s?

   [1 mark]

   • A5 m s⁻¹
   • B4 m s⁻¹
   • C0.25 m s⁻¹
   • D100 m s⁻¹

   (b)

   What is the velocity of the cyclist from t = 8 s to t = 14 s?

   [1 mark]

   • A+3.33 m s⁻¹
   • B−2.5 m s⁻¹
   • C−1.43 m s⁻¹
   • D−3.33 m s⁻¹

   (c)

   Find the total distance the cyclist has travelled by t = 14 s, and her displacement from the start at that time.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A lift starts from rest at the ground floor. Its acceleration–time graph consists of three horizontal sections: an acceleration of 1.5 m s⁻² from t = 0 to t = 4 s, no acceleration from t = 4 s to t = 10 s, and an acceleration of −2 m s⁻² from t = 10 s to t = 13 s.

   (a)

   Find the greatest speed of the lift, and show that the lift is at rest at t = 13 s.

   [3 marks]

   (b)

   Find the total distance travelled by the lift.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A train travels between two stations on a straight level track. Its speed–time graph is a trapezium. The train accelerates uniformly from rest at 0.5 m s⁻² until it reaches a speed of V m s⁻¹, travels at this constant speed, and then decelerates uniformly at 1 m s⁻² to rest. The journey takes 160 s and the distance between the stations is 2600 m.

   (a)

   Find, in terms of $V$, the time taken to accelerate, the time taken to decelerate and the time at constant speed. Hence show that $3V^2-320V+5200=0$.

   [6 marks]

   (b)

   Solve the equation in (a), rejecting any root that is not possible. Hence find the distance travelled at constant speed and the average speed over the whole journey.

   [6 marks]

   Total for question 4: 12 marks

End of questions