(A Math) 2025 CCHY PRELIMS P2 Q10
(A Math) 2025 CCHY PRELIMS P2 Q10
Secondary 4
9 marks
A particle travels in a straight line so that its displacement, \(s\) m, from \(O\) at time \(t\) seconds, where \(t \ge 0\), is modelled by \(s=t^3-\frac{9}{2}t^2+6t+1\).
- Find the values of \(t\) for which the particle is instantaneously at rest.[3]
- The particle’s acceleration is \(15\text{ m/s}^2\) at \(T\) seconds. Find the total distance travelled by the particle in the interval \(t=0\) to \(t=T\).[4]
- Explain clearly why the answer found in part (b) should not be obtained by finding the value of \(s\) when \(t=T\).[2]
Solution:
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Answer:(a) \(t=1\text{ s}\) or \(t=2\text{ s}\) (b) \(17\text{ m}\) (c) \(s(T)\) gives displacement from \(O\), not total distance. The particle changes direction at \(t=1\) and \(t=2\), so the distances in each interval must be added.
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