A particle moves from point $P$ towards point $O$. The speed of the particle, $t$ seconds afte

Question

A particle moves from point $P$ towards point $O$. The speed of the particle, $t$ seconds after passing point $P$, can be modelled by the formula $v=(k-2t)^n$, where $k$ and $n$ are constants. Find an expression for the acceleration of the particle in terms of $k$, $t$ and $n$.[1] The particle has a speed of $27$ m/s when $t=3.5$ and comes to instantaneous rest $4.8$ metres to the right of point $O$ when $t=8$. Find the value of $k$ and of $n$.[3] Using the values of $k$ and $n$ found in part (b), find the total distance travelled by the particle in the first $8$ seconds.[4] Explain whether the given model can continue to describe the motion of the particle after $8$ seconds.[1] Assume $n>0$ and take the direction from $P$ towards $O$ as positive. Before the first rest, the given speed equals the signed velocity in this convention.

Accepted Answer

(a) $a=-2n(k-2t)^{n-1}$ (b) $k=16,\ n=\dfrac{3}{2}$ (c) $205\text{ m}$ (d) No, since $(16-2t)^{\frac{3}{2}}$ is not real for $t>8$.

2025 PHS PRELIMS P2 Q11

2025 PHS PRELIMS P2 Q11

Solution:

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