- In this question you must show all stages in your working. Solutions relying entirely on calculator technology are not acceptable.
A particle \(P\) is moving along the \(x\)-axis.
At time \(t\) seconds, where \(0 \leqslant t \leqslant \frac { 2 } { 3 } , P\) is \(x\) metres from the origin 0 and is moving with velocity \(\mathrm { v } \mathrm { m } \mathrm { s } ^ { - 1 }\) in the positive x direction where
$$v = ( 2 x + 1 ) ^ { \frac { 3 } { 2 } }$$
When \(\mathrm { t } = 0 , \mathrm { P }\) passes through 0 .
- Find the value of x when the acceleration of P is \(243 \mathrm {~m} \mathrm {~s} ^ { - 2 }\)
- Find v in terms of t .