Mathematics 9709 · AS & A Level · Kinematics of motion in a straight line
Kinematics of motion in a straight line — practice question
Particle $P$ departs from point $O$ and travels along a straight line. $P$’s velocity $t\,\text{s}$ after leaving $O$ is $v\,\text{m s}^{-1}$, where $v = 0.16t^{3} - 0.016t^{2}$. $P$ is momentarily at rest at point $A$.
(i)[1]
Verify that the value of $t$ when $P$ is at $A$ is $100$.
(ii)[4]
Find the maximum speed of $P$ in the interval $0 \le t \le 100$.
(iii)[3]
Find the length of $OA$.
(iv)[2]
Find the value of $t$ when $P$ passes through $O$ after returning from $A$.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Substitutes $t = 100$ into $v(t)$ and gets zero” …