A particle travels in a straight line from a point $P$ to a point $Q$. Its velocity $t$ seconds after leaving $P$ is $vm{\text{ }}{s^{ - 1}}$ where $v = 4t - \frac{4}{{16}}{t^3}$. The distance $PQ$ is $64{\text{ }}m$.
a) Find the time taken for the particle to travel from $P$ to $Q$.
b) Find the set of values of $t$ for which the acceleration of the particle is positive.
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