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<p>A particle moves in a straight line so that its displacement, \(s\) meters, from a fixed point \(O\) on the straight line is given by \(s=-t^3+3t^2+9t-5\) for \(t \le 4\), where \(t\) is the time in seconds after passing through a point \(P\) on the line.</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">Find</span></div><ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">the distance \(OP\),</span></div></li><li><div class="list-item-content"><span class="list-item-text">the distance from \(O\) of the particle when it is instantaneously at rest,</span></div></li><li><div class="list-item-content"><span class="list-item-text">the total distance travelled by the particle during the first \(4\) seconds,</span></div></li><li><div class="list-item-content"><span class="list-item-text">the velocity of the particle when \(t=4\).</span></div></li></ol></li><li><div class="list-item-content"><span class="list-item-text">At \(t=4\) the acceleration of the particle is changed to \((2t-10)\) \(\mathrm{ms}^{-2}\) the instantaneous velocity remaining unchanged and it finally stops at \(Q\) when \(t=T\). Find the value of \(T\).</span></div></li></ol>

A particle moves in a straight line so that its displacement, \(s\) meters, from a fixed point \(O\) on the straight line is given by \(s=-t^3+3t^2+9t-5\) for \(t \le 4\), where \(t\) is the time in seconds after passing through a point \(P\) on the line.

the distance from \(O\) of the particle when it is instantaneously at rest,

the total distance travelled by the particle during the first \(4\) seconds,

the velocity of the particle when \(t=4\).

At \(t=4\) the acceleration of the particle is changed to \((2t-10)\) \(\mathrm{ms}^{-2}\) the instantaneous velocity remaining unchanged and it finally stops at \(Q\) when \(t=T\). Find the value of \(T\).

Kinematics - Given the Displacement Function

Question 777f3639

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