Work, energy and powerEdexcel International A Level Further Maths: Subtopic test

1. 1
   A car of mass $1200$ kg moves along a straight horizontal road. The engine works at a constant power of $24$ kW and the resistance to motion is a constant $800$ N.

   (a)

   Find the driving force of the engine when the car is travelling at $15$ m s$^{-1}$.

   [1 mark]

   • A$360\,000$ N
   • B$1.6$ N
   • C$800$ N
   • D$1600$ N

   (b)

   Find the acceleration of the car when it is travelling at $15$ m s$^{-1}$.

   [1 mark]

   • A$1.33$ m s$^{-2}$
   • B$0.667$ m s$^{-2}$
   • C$2.00$ m s$^{-2}$
   • D$0.5$ m s$^{-2}$

   (c)

   Find the increase in the car's kinetic energy as its speed increases from $15$ m s$^{-1}$ to $30$ m s$^{-1}$.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A box of mass $5$ kg is pulled from rest up a line of greatest slope of a rough plane inclined at $20^\circ$ to the horizontal, by a constant force of $40$ N acting parallel to the plane. A constant frictional force of $8$ N opposes the motion. Take $g=9.8$ m s$^{-2}$. The box moves $6$ m up the plane.

   (a)

   Find the work done against gravity as the box moves up the plane.

   [1 mark]

   • A$294$ J
   • B$276$ J
   • C$101$ J
   • D$16.8$ J

   (b)

   Find the kinetic energy of the box after it has moved $6$ m.

   [1 mark]

   • A$91.4$ J
   • B$192$ J
   • C$139$ J
   • D$389$ J

   (c)

   Find the speed of the box after it has moved $6$ m.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A lorry of mass $6000$ kg moves up a straight road inclined at an angle $\alpha$ to the horizontal, where $\sin\alpha=\frac{1}{20}$. The resistance to motion is a constant $1500$ N. Take $g=9.8$ m s$^{-2}$.

   (a)

   The lorry travels up the road at a constant speed of $12$ m s$^{-1}$. Find the power of the engine.

   [3 marks]

   (b)

   At one instant the lorry is moving up the road at $8$ m s$^{-1}$ with the engine working at the power found in (a). Find the acceleration of the lorry at this instant.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A particle of mass $0.4$ kg is projected with speed $12$ m s$^{-1}$ up a line of greatest slope of a rough plane inclined at $30^\circ$ to the horizontal. The coefficient of friction between the particle and the plane is $0.25$. The particle comes to instantaneous rest and then slides back down. Take $g=9.8$ m s$^{-2}$.

   (a)

   Use the work-energy principle to find the distance the particle travels up the plane before it comes to instantaneous rest.

   [6 marks]

   (b)

   Find the speed of the particle when it returns to its starting point.

   [6 marks]

   Total for question 4: 12 marks

End of questions