(i)[4]
Show that $s = t^3 - 6t^2 + pt + q$, where $p$ and $q$ are constants to be found.
(ii)[2]
Find the values of $t$ for which $P$ is instantaneously at rest.
(iii)[4]
Find the total distance travelled by $P$ over the interval $0 \leq t \leq 4$.
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 in a straight line. Its acceleration $a\,\text{m s}^{-2}$ at time $t\,\text{s}$ is $a = 6t - 12$. The displacement of $P$ from a fixed point $O$ on the line is $s\,\text{m}$. It is known that $s = 5$ when $t = 1$ and $s = 1$ when $t = 3$.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Integrates the acceleration to obtain the velocity $v = 3t^2 - 12t + C$” …
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