A particle $P$ of mass $0.4{\text{ }}kg$ is projected horizontally with velocity $8{\text{ }}m{\text{ }}{s^{ - 1}}$ from a point $O$ on a smooth horizontal surface. The motion of $P$ is opposed by a resisting force of magnitude $0.2{v^2}{\text{ }}N$, where $vm{\text{ }}{s^{ - 1}}$ is the velocity of $P$ at time $t\,s$ after projection.
a) Show that $v = \frac{8}{{1 + 4t}}$.
b) Calculate the distance $OP$ when $t = 1.5$.
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