Mathematics 9709 · AS & A Level · Kinematics of motion in a straight line
Kinematics of motion in a straight line — practice question
A vehicle begins from rest at point $O$ and travels along a straight line. Its speed $v\,\text{m s}^{-1}$ after $t$ seconds from leaving $O$ is given by the following: when $0 \leq t \leq 60$, $v = k_1 t - 0.005t^2$; and when $t > 60$, $v = \frac{k_2}{\sqrt{t}}$. During the first $60\,\text{s}$, the vehicle covers a distance of $540\,\text{m}$.
(i)[5]
Find the value of the constant $k_1$ and show, by calculation, that $k_2 = 12\sqrt{60}$.
(ii)[2]
Find a formula in terms of $t$ for the total distance travelled when $t \geq 60$.
(iii)[3]
Find the speed of the vehicle once it has travelled a total distance of $1260\,\text{m}$.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Use $s=\int v\,dt$ with the velocity written in separate parts” …