Mathematics 9709 · AS & A Level · Kinematics of motion in a straight line
Kinematics of motion in a straight line — practice question
A particle $P$ leaves point $O$ and then moves along a straight line. At time $t\,\text{s}$ after leaving $O$, the velocity of $P$ is $k(60t^2 - t^3)\,\text{m s}^{-1}$, where $k$ is a constant. The maximum velocity of $P$ is $6.4\,\text{m s}^{-1}$.
(i)[3]
Show that the constant is $k = 0.0002$.
(ii)[5]
At a point $A$ on the line, $P$ comes to instantaneous rest. Determine $OA$.
(iii)[2]
Find the magnitude of the acceleration of $P$ at point $A$.
(iv)[2]
Find the speed of $P$ when it next passes through $O$.
Worked solution & mark scheme
This 12-mark question has a full step-by-step worked solution and mark scheme. One marking point: “From $\frac{dv}{dt} = k(120t - 3t^2)$” …