(i)[7]
Find the values of $T_1$ and $T_2$, together with the distance $OP$ when $t = T_2$.
(ii)[3]
Find the velocity of $P$ when $t = T_2$, then sketch the velocity-time graph for the motion of $P$.
Mathematics 9709 · AS & A Level · Kinematics of motion in a straight line
Kinematics of motion in a straight line — practice question
A particle $P$ moves along a straight line. At time $t = 0$, where $t$ is measured in seconds, it passes through point $O$ on the line with velocity $5\,\text{m}\,\text{s}^{-1}$. Once $P$ has left $O$, its velocity is given by $(0.002t^{3} - 0.12t^{2} + 1.8t + 5)\,\text{m}\,\text{s}^{-1}$. The velocity of $P$ is increasing for $0 < t < T_1$ and for $t > T_2$, and it is decreasing for $T_1 < t < T_2$.