<p>A particle travels in a straight line so that its displacement, \(s\) m, from \(O\) at time \(t\) seconds, where&nbsp;\(t \ge 0\), is modelled by \(s = t^3 - \frac{9}{2}t^2 + 6t + 1\).</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">Find the values of \(t\) for which the particle is instantaneously at rest.</span><span class="inline-marks">[3]</span></div></li><li><div class="list-item-content"><span class="list-item-text">The particle's acceleration is \(15\) m/s\({}^2\) at \(T\) seconds. Find the total distance travelled by the particle in the interval \(t = 0\) to \(t = T\).</span><span class="inline-marks">[4]</span></div></li><li><div class="list-item-paragraph">Explain clearly why the answer found in part (b) should not be obtained by finding the value ofs when t = T<span class="inline-marks">[2]</span></div></li></ol>

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.

The particle's acceleration is \(15\) m/s\({}^2\) at \(T\) seconds. Find the total distance travelled by the particle in the interval \(t = 0\) to \(t = T\).

Explain clearly why the answer found in part (b) should not be obtained by finding the value ofs when t = T

2025 CHHY PRELIMS P2 Q10

2025 CHHY PRELIMS P2 Q10