Mathematics 9709 · AS & A Level · Energy, work and power
Energy, work and power — practice question
A lorry with mass $16\,000\,\text{kg}$ travels up the straight hill $ABCD$, which is inclined at angle $\theta$ to the horizontal and satisfies $\sin\theta = \frac{1}{25}$. While moving from $A$ to $B$, the driving force of the lorry does $1200\,\text{kJ}$ of work, and the resistive force remains constant at $1240\,\text{N}$. Its speed is $15\,\text{m s}^{-1}$ at $A$ and $12\,\text{m s}^{-1}$ at $B$.
(i)[5]
Find the length of $AB$.
(ii)[1]
For the motion from $B$ to $D$ the lorry's increase in potential energy is $2400\,\text{kJ}$. Find the distance $BD$.
(iii)[4]
While the lorry travels from $B$ to $D$, the driving force stays constant at $7200\,\text{N}$. Between $B$ and $C$, the resistance to motion is constant at $1240\,\text{N}$, and between $C$ and $D$, it is constant at $1860\,\text{N}$. If the speed of the lorry at $D$ is $7\,\text{m s}^{-1}$, find the distance $BC$.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Calculates the KE loss from $\tfrac12 16000(15^2-12^2)” …