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

1. 1
   A stone of mass $0.2$ kg is thrown vertically upwards from ground level with speed $15$ m s$^{-1}$. Air resistance may be ignored. Take $g=9.8$ m s$^{-2}$.

   (a)

   Find the kinetic energy of the stone when it is thrown.

   [1 mark]

   • A$3$ J
   • B$1.5$ J
   • C$45$ J
   • D$22.5$ J

   (b)

   Find the greatest height reached by the stone above the ground.

   [1 mark]

   • A$23.0$ m
   • B$11.5$ m
   • C$2.30$ m
   • D$1.53$ m

   (c)

   Find the speed of the stone when it is $5$ m above the ground, on the way up.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A car of mass $1200$ kg has its engine working at a constant power of $24$ kW. The resistance to the car's motion is constant at $600$ N on every road.

   (a)

   Find the maximum speed of the car on a level road.

   [1 mark]

   • A$40$ m s$^{-1}$
   • B$25$ m s$^{-1}$
   • C$0.025$ m s$^{-1}$
   • D$1.44\times10^{7}$ m s$^{-1}$

   (b)

   On a level road, find the acceleration of the car when its speed is $20$ m s$^{-1}$.

   [1 mark]

   • A$1.0$ m s$^{-2}$
   • B$-0.5$ m s$^{-2}$
   • C$0.5$ m s$^{-2}$
   • D$399.5$ m s$^{-2}$

   (c)

   The car climbs a straight road inclined at an angle $\alpha$ to the horizontal, where $\sin\alpha=\frac{1}{20}$, at a constant speed. Find this speed.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A particle of mass $4$ kg is projected up a line of greatest slope of a rough plane that is inclined at $30^\circ$ to the horizontal, with initial speed $8$ m s$^{-1}$. The coefficient of friction between the particle and the plane is $0.3$. Take $g=9.8$ m s$^{-2}$.

   (a)

   Find the magnitude of the frictional force acting on the particle.

   [3 marks]

   (b)

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

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A lorry of mass $5000$ kg moves with its engine working at a constant power of $40$ kW. When the lorry has speed $v$ m s$^{-1}$, the resistance to its motion is $100v$ N, on any road. Take $g=9.8$ m s$^{-2}$.

   (a)

   The lorry travels along a horizontal road.
   (i) Find the maximum speed of the lorry.
   (ii) Find the acceleration of the lorry when its speed is $10$ m s$^{-1}$.

   [6 marks]

   (b)

   The lorry now moves on a straight road inclined at an angle $\theta$ to the horizontal, where $\sin\theta=\frac{1}{20}$.
   (i) With the engine switched off, the lorry moves down the road at a constant speed. Find this speed.
   (ii) With the engine working at $40$ kW, the lorry moves up the road at a constant speed. Find this speed.

   [6 marks]

   Total for question 4: 12 marks

End of questions