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 through a point $O$. When the time is $t\text{ s}$, the velocity of $P$, $v\text{ m s}^{-1}$, is given by $v = qt + rt^2$, where $q$ and $r$ are constants. The particle’s velocity is $4\text{ m s}^{-1}$ at both $t = 1$ and $t = 2$.
(i)[4]
Demonstrate that, for $t = 0.5$, the acceleration of $P$ is $4\text{ m s}^{-2}$.
(ii)[2]
Determine the values of $t$ for which $P$ is instantaneously at rest.
(iii)[4]
The particle is at $O$ when $t = 3$. Determine the distance of $P$ from $O$ when $t = 0$.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Form equations by using $v=4$ at $t=1$ and $t=2$” …