Mathematics 9709 · AS & A Level · Kinematics of motion in a straight line
Kinematics of motion in a straight line — practice question
A particle travels along a straight line, beginning from rest at the point $O$ and arriving momentarily at rest at the point $P$. After $t\,\text{s}$ from leaving $O$, its velocity is $v\,\text{m s}^{-1}$, where $v = 0.6t^2 - 0.12t^3$.
(i)[5]
Demonstrate that $OP = 6.25\,\text{m}$.
(ii)[5]
At a different time, the particle again travels along the same straight line. For this motion, the displacement after $t\,\text{s}$ from leaving $O$ is $s\,\text{m}$, where $s = kt^3 + ct^5$. It is stated that the particle goes through point $P$ with velocity $1.25\,\text{m s}^{-1}$ at time $t = 5$. Determine the values of the constants $k$ and $c$.
(iii)[2]
Determine the acceleration of the particle when $t = 5$.
Worked solution & mark scheme
This 12-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Trying $v = 0$ and obtaining $0.6t^2 - 0.12t^3 = 0$” …