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<p>A particle travelling in a straight line starts from rest at point \(O\) and has acceleration (in \(\text{m s}^{-2}\)) <br>Modelled by the equation \(a = 12 - 8t\), where&nbsp;\(t\) is measured in seconds.</p>
<ol class="abc-list"><li data-list-item-id="item-a" data-list-item-path="item-a"><div class="list-item-paragraph">Find an expression for the velocity of the particle at time \(t\).</div></li><li data-list-item-id="item-b" data-list-item-path="item-b"><div class="list-item-paragraph">Find an expression for the position of the particle at time \(t\).</div></li><li data-list-item-id="item-c" data-list-item-path="item-c"><div class="list-item-paragraph">Find its furthest distance from \(O\) in a positive direction during the subsequent motion.</div></li><li data-list-item-id="item-d" data-list-item-path="item-d"><div class="list-item-paragraph">Find the time taken for the particle to return to \(O\), and its velocity at that time.</div></li><li data-list-item-id="item-e" data-list-item-path="item-e"><div class="list-item-paragraph">Describe the motion of the particle after it passes through \(O\) for the second time.</div></li></ol>

A particle travelling in a straight line starts from rest at point \(O\) and has acceleration (in \(\text{m s}^{-2}\)) 
Modelled by the equation \(a = 12 - 8t\), where \(t\) is measured in seconds.

Find an expression for the velocity of the particle at time \(t\).

Find an expression for the position of the particle at time \(t\).

Find its furthest distance from \(O\) in a positive direction during the subsequent motion.

Find the time taken for the particle to return to \(O\), and its velocity at that time.

Describe the motion of the particle after it passes through \(O\) for the second time.

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