Mathematics 9709 · AS & A Level · Kinematics of motion in a straight line
Kinematics of motion in a straight line — practice question
Particle $P$ moves along a straight line and begins from rest at point $O$. After $t\,\text{s}$ from leaving $O$, its acceleration is $a\,\text{m s}^{-2}$, with $a = 0.3t^{\frac{1}{2}}$ for $0 \le t \le 4$, and $a = -kt^{-3/2}$ for $4 < t \le T$, where $k$ and $T$ are constants.
(a)[2]
Determine the velocity of $P$ when $t = 4$.
(b)[4]
It is stated that the velocity of $P$ is unchanged at $t = 4$ and that at $t = 16$ the velocity of $P$ is $0.3\,\text{m s}^{-1}$. Show that $k = 2.6$ and determine an expression, in terms of $t$, for the velocity of $P$ for $4 \le t \le T$.
(c)[2]
Given that $P$ is instantaneously at rest at $t = T$, determine the exact value of $T$.
(d)[4]
Find the total distance travelled over $t = 0$ to $t = T$.
Worked solution & mark scheme
This 12-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Integrating acceleration gives velocity $v=0.2t^{5/2}+c$” …