Mathematics 9709 · AS & A Level · Newton's laws of motion
Newton's laws of motion — practice question
A car of mass $1200\,\text{kg}$ is moving at speed $v\,\text{m s}^{-1}$, and the resistive force has magnitude $kv\,\text{N}$. The engine’s maximum power is $92.16\,\text{kW}$. The car is moving on a straight, horizontal road.
(a(i))[1]
The car’s largest possible constant speed is $48\,\text{m s}^{-1}$. Show that $k = 40$.
(a(ii))[3]
At the moment when the speed is $45\,\text{m s}^{-1}$, find the car’s greatest possible acceleration.
(b)[4]
The car now moves with constant speed up a hill that is inclined at an angle of $\sin^{-1} 0.15$ to the horizontal. Find the car’s greatest possible speed as it goes uphill.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Use $\text{Power}=k\times48^2=92160$ to determine $k$” …