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

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 \(P\).

Kinematics

Kinematics