Mathematics 9709 · AS & A Level · Energy, work and power

Energy, work and power — practice question

A train with mass $150\,000\,\text{kg}$ moves up a straight slope at an angle of $\alpha^{\circ}$ to the horizontal, with a constant driving force of $16\,000\,\text{N}$. When the train is at point $A$ on the slope, its speed is $45\,\text{m s}^{-1}$. Point $B$ is $500\,\text{m}$ farther along the slope than $A$. At $B$, the train's speed is $42\,\text{m s}^{-1}$. A resistance force acts on the train, and between $A$ and $B$ the train does $4 \times 10^{6}\,\text{J}$ of work against this resistance force.
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Find the value of $\alpha$ from this information.

Worked solution & mark scheme

This 5-mark question has a full step-by-step worked solution and mark scheme. One marking point: Correct expression for the increase in PE $=150000g\times500\sin\alpha$

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