- At time \(t\) seconds, where \(0 \leq t \leq T\), a particle, \(P\), moves so that its velocity \(v m s ^ { - 1 }\) is given by
$$v = 7.2 t - 0.45 t ^ { 2 }$$
When \(t = 0\) the particle is sitting stationary at a displacement of \(\mathrm { d } m\) from a point O .
The particle's acceleration is zero when \(t = T\).
- Find the value of \(T\).
For \(t \geq T\), the particle moves with a velocity \(v = 48 - 2.4 t m s ^ { - 1 }\).
- Find the time when \(P\) is at its maximum displacement from O . The particle passes through the point O when \(t = 38\).
- Find \(d\).
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