ImpulseAQA A-Level Further Maths: Subtopic test

1. 1
   A ball of mass $0.4$ kg is moving in a straight line along smooth horizontal ground at $6$ m s⁻¹. It is struck by a bat, which exerts a constant force in the direction of motion for $0.05$ s. Immediately afterwards the ball is moving at $15$ m s⁻¹ in the same direction.

   (a)

   Find the magnitude of the impulse the bat exerts on the ball.

   [1 mark]

   • A$2.4$ N s
   • B$6$ N s
   • C$8.4$ N s
   • D$3.6$ N s

   (b)

   Find the magnitude of the force exerted by the bat.

   [1 mark]

   • A$72$ N
   • B$3.6$ N
   • C$0.18$ N
   • D$168$ N

   (c)

   The ball is struck again by the same force, acting for $0.08$ s on the ball moving at $6$ m s⁻¹. Find the speed of the ball afterwards.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A particle of mass $2$ kg moves in a straight line on a smooth horizontal surface. At time $t$ seconds, for $0\le t\le4$, a force of magnitude $F=6t^2$ newtons acts on it in the direction of motion. When $t=0$ the particle is moving at $3$ m s⁻¹.

   (a)

   Find the magnitude of the impulse of the force over the interval $0\le t\le4$.

   [1 mark]

   • A$96$ N s
   • B$128$ N s
   • C$384$ N s
   • D$48$ N s

   (b)

   Find the speed of the particle when $t=4$.

   [1 mark]

   • A$64$ m s⁻¹
   • B$131$ m s⁻¹
   • C$67$ m s⁻¹
   • D$61$ m s⁻¹

   (c)

   Find the speed of the particle when $t=2$.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A tennis ball of mass $0.06$ kg is travelling horizontally at $20$ m s⁻¹ when it is hit by a racket. The ball leaves the racket at $30$ m s⁻¹ in the opposite direction. The ball is in contact with the racket for $0.004$ s.

   (a)

   Find the magnitude and direction of the impulse exerted by the racket on the ball.

   [3 marks]

   (b)

   (i) Find the average force exerted by the racket on the ball.
   (ii) The weight of the ball was ignored in part (a). Taking $g=9.8$ m s⁻², justify this.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A particle of mass $0.5$ kg is moving on a smooth horizontal plane with velocity $(6\mathbf{i}-2\mathbf{j})$ m s⁻¹ when it is struck by a bat, which exerts an impulse $\mathbf{I}$ N s on it. Immediately afterwards the velocity of the particle is $(-2\mathbf{i}+4\mathbf{j})$ m s⁻¹, where $\mathbf{i}$ and $\mathbf{j}$ are perpendicular horizontal unit vectors.

   (a)

   (i) Find the impulse $\mathbf{I}$.
   (ii) Find the magnitude of $\mathbf{I}$, and the angle between $\mathbf{I}$ and the vector $-\mathbf{i}$.

   [6 marks]

   (b)

   The impulse $\mathbf{I}$ acted for $0.02$ s with a constant force. Find the magnitude of the force. The particle later receives a second impulse $(\mathbf{i}-5\mathbf{j})$ N s. Find its new velocity and speed.

   [6 marks]

   Total for question 4: 12 marks

End of questions