<p>A particle moves in a straight line so that, \(t\) seconds after passing through a fixed point \(O\), its velocity, \(v\) m/s, is given by \(v = k \cos 2t\), where&nbsp;\(k\) is a constant. When&nbsp;\(t = \frac{\pi}{12}\), the acceleration is \(-6\) m/s.</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">Find the value of \(k\).</span><span class="inline-marks">[2]</span></div></li><li><div class="list-item-content"><span class="list-item-text">The particle is first at rest at point \(P\). Find the value of \(t\) when the particle is at point \(P\).</span><span class="inline-marks">[2]</span></div></li><li><div class="list-item-paragraph">Find the distance travelled by the particle from O to P.<span class="inline-marks">[3]</span></div></li></ol>

A particle moves in a straight line so that, \(t\) seconds after passing through a fixed point \(O\), its velocity, \(v\) m/s, is given by \(v = k \cos 2t\), where \(k\) is a constant. When \(t = \frac{\pi}{12}\), the acceleration is \(-6\) m/s.

The particle is first at rest at point \(P\). Find the value of \(t\) when the particle is at point \(P\).

Find the distance travelled by the particle from O to P.

2025 MGS PRELIMS P2 Q7

2025 MGS PRELIMS P2 Q7