- A particle is moving along the \(x\)-axis. At time \(t\) seconds the particle is \(x\) metres from the origin, \(O\), and its velocity \(v \mathrm {~ms} ^ { - 1 }\) is given by
$$v = \frac { 24 } { 4 x + 9 }$$
- Find, in terms of \(x\), an expression for the acceleration of the particle at time \(t \mathrm {~s}\).
- At \(t = T\) the acceleration of the particle is \(- \frac { 4 } { 3 } \mathrm {~ms} ^ { - 2 }\).
- Determine the value of \(x\) when \(t = T\).
- Given that \(x = - 2\) when \(t = 0\), find an expression for \(t\) in terms of \(x\) and hence find the value of \(T\).