Mathematics 9709 · AS & A Level · Kinematics of motion in a straight line
Kinematics of motion in a straight line — practice question
A particle $P$ is initially at rest and then travels in a straight line away from point $O$. At time $t\,\text{s}$ after leaving $O$, the velocity of $P$, $v\,\text{m s}^{-1}$, is $v = bt + ct^{\frac{3}{2}}$, where $b$ and $c$ are constants. The velocity of $P$ is $8\,\text{m s}^{-1}$ when $t = 4$ and $13.5\,\text{m s}^{-1}$ when $t = 9$.
(a)[1]
Show that $b = 3$ while $c = -0.5$.
(b)[2]
Find the acceleration of $P$ at $t = 1$.
(c)[5]
Find the positive value of $t$ when $P$ is instantaneously at rest and determine the distance of $P$ from $O$ at this moment.
(d)[3]
Find the speed of $P$ at the moment it returns to $O$.
Worked solution & mark scheme
This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Write down two correct equations and state $b = 3$ and $c = -0.5$.” …