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. It begins at a point $O$ on the line and is back at $O\,100\,\text{s}$ later. The velocity of $P$ is $v\,\text{m s}^{-1}$ at time $t\,\text{s}$ after leaving $O$, where $v = 0.0001t^{3} - 0.015t^{2} + 0.5t$.
(i)[2]
Show that $P$ is instantaneously at rest at $t = 0$, $t = 50$ and $t = 100$.
(ii)[7]
Find the values of $v$ at the times when the acceleration of $P$ is zero, and sketch the velocity-time graph for the motion of $P$ for $0 \leq t \leq 100$.
(iii)[4]
Find the greatest distance of $P$ from $O$ over $0 \leq t \leq 100$.
Worked solution & mark scheme
This 13-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Factorise $v(t)$ or evaluate it at the specified times” …