Mathematics 9709 · AS & A Level · Kinematics of motion in a straight line

Kinematics of motion in a straight line — practice question

A car with mass $1250\,\text{kg}$ is moving on a level straight road. Its engine delivers constant power of $24\,\text{kW}$, and the resistive force on the car is a constant $R\,\text{N}$. As the car goes through point $A$ on the road, its speed is $20\,\text{m s}^{-1}$ and its acceleration is $0.32\,\text{m s}^{-2}$.
(i)[3]

Determine the value of $R$.

(ii)[2]

The car keeps moving faster and passes point $B$ on the road with speed $29.9\,\text{m s}^{-1}$. It later goes through point $C$. Determine the acceleration of the car at $B$, giving the answer in $\text{m s}^{-2}$ correct to $3$ decimal places.

(iii)[2]

Show that, while the car’s speed is increasing, it cannot reach $30\,\text{m s}^{-1}$.

(iv)[1]

Explain why the speed of the car is approximately constant between $B$ and $C$.

(v)[1]

State a value of the approximately constant speed, and the maximum possible error in this value at any point between $B$ and $C$.

(vi(a))[2]

The work done by the car’s engine while travelling from $B$ to $C$ is $1200\,\text{kJ}$. Assuming the car’s speed is constant from $B$ to $C$, find the approximate time taken for the car to travel from $B$ to $C$.

(vi(b))[2]

By assuming the car’s speed is constant from $B$ to $C$, find an approximation for the distance $BC$.

Worked solution & mark scheme

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