<p>A particle, \(P\), travels in a straight line so that at time \(t\) seconds, its velocity, \(v\) m/s, is given by \[v = \cos(\frac{\pi}{4}t + \frac{\pi}{6}).\] The initial displacement of \(P\) from a fixed point \(O\) is \(\frac{1}{\pi}\) m.</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">Find the initial velocity of \(P\), giving your answer in exact value.</span><span class="inline-marks">[1]</span></div></li><li><div class="list-item-content"><span class="list-item-text">Find the first two values of \(t\) when&nbsp;\(P\) comes to instantaneous rest.</span><span class="inline-marks">[3]</span></div></li><li><div class="list-item-paragraph">Find the distance travelled by \(P\)  in the first \(4\) seconds.<span class="inline-marks">[4]</span></div></li></ol>

A particle, \(P\), travels in a straight line so that at time \(t\) seconds, its velocity, \(v\) m/s, is given by \[v = \cos(\frac{\pi}{4}t + \frac{\pi}{6}).\] The initial displacement of \(P\) from a fixed point \(O\) is \(\frac{1}{\pi}\) m.

Find the initial velocity of \(P\), giving your answer in exact value.

Find the first two values of \(t\) when \(P\) comes to instantaneous rest.

Find the distance travelled by \(P\)  in the first \(4\) seconds.

2025 SCGS PRELIMS P2 Q7

2025 SCGS PRELIMS P2 Q7