A particle $P$ starts from a fixed point $O$ at time $t = 0$, where $t$ is in seconds, and moves with constant acceleration in a straight line. The initial velocity of $P$ is $1.5{\text{ }}m{\text{ }}{s^{ - 1}}$ and its velocity when $t = 0$ is $3.5{\text{ }}m{\text{ }}{s^{ - 1}}$.
a) Find the displacement of $P$ from $O$ when $t = 10$.
Another particle $Q$ also starts from $O$ when $t = 0$ and moves along the same straight line as $P$. The acceleration of $Q$ at time $t$ is $0.03t{\text{ }}m{\text{ }}{s^{ - 2}}$.
b) Given that $Q$ has the same velocity as $P$ when $t = 10$, show that it also has the same displacement from $O$ as $P$ when $t = 10$.
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