- In this question you must show all stages of your working. Solutions relying on calculator technology are not acceptable.
A particle \(P\) is moving in a straight line.
At time \(t\) seconds, the speed, \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\), of \(P\) is given by the continuous function
$$v = \begin{cases} \sqrt { 2 t + 1 } & 0 \leqslant t \leqslant k
\frac { 3 } { 4 } t & t > k \end{cases}$$
where \(k\) is a constant.
- Show that \(k = 4\), explaining your method carefully.
- Find the acceleration of \(P\) when \(t = 1.5\)
At time \(t = 0 , P\) passes through the point \(O\)
- Find the distance of \(P\) from \(O\) when \(t = 8\)