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 is at rest at $A$ when it sets off and it is brought to rest instantaneously at $B$. The velocity of $P$ after $t$ seconds from leaving $A$ is $v\,\text{m s}^{-1}$, where $v = 6t^2 - kt^3$ and $k$ is a constant.
(i)[2]
Determine an expression for the displacement of $P$ from $A$ in terms of $t$ and $k$.
(ii)[1]
Determine an expression for $t$ in terms of $k$ when $P$ is at $B$.
(iii)[2]
Given that the distance $AB$ is $108\,\text{m}$, determine $k$.
(iv)[3]
Determine the maximum value of $v$ while the particle is travelling from $A$ towards $B$.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Start from $s=\int v\,dt$” …