Mathematics 9709 · AS & A Level · Energy, work and power
Energy, work and power — practice question
A car with mass $1200\,\text{kg}$ can move at a maximum constant speed of $60\,\text{m s}^{-1}$ on a straight horizontal road. When the car is moving at $v\,\text{m s}^{-1}$, the resistive force has magnitude $35v\,\text{N}$.
(i)[2]
Find the car’s greatest possible power.
(ii)[3]
The car moves on a straight horizontal road. Show that, at the instant when its speed is $30\,\text{m s}^{-1}$, the car’s greatest possible acceleration is $2.625\,\text{m s}^{-2}$.
(iii)[5]
The car moves up a hill at constant speed, where the hill is inclined at an angle of $\sin^{-1}\!\left(\frac{7}{48}\right)$ to the horizontal. Find the car’s greatest possible speed.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Driving force found from $35 \times 60$” …