(a)[3]
Assuming there are no instantaneous changes in velocity, determine $p$ and $q$.
(b)[3]
Draw the velocity-time graph.
(c)[5]
Determine the total distance covered by $P$ in the $14\,\text{s}$.
Mathematics 9709 · AS & A Level · Kinematics of motion in a straight line
Kinematics of motion in a straight line — practice question
A particle $P$ travels along a straight line from a point $O$ and is brought to rest $14\,\text{s}$ afterwards. If $t\,\text{s}$ have elapsed since leaving $O$, the velocity $v\,\text{m s}^{-1}$ of $P$ is defined by
$v = pt^2 - qt \quad 0 \leq t \leq 6,$
$v = 63 - 4.5t \quad 6 \leq t \leq 14,$
where $p$ and $q$ are positive constants. The acceleration of $P$ is zero when $t = 2$.