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 and begins at point $O$. Its velocity $v\text{ m s}^{-1}$ at time $t\text{ s}$ is defined by
$v = 12t - 4t^2$ for $0 \le t \le 2$, and
$v = 16 - 4t$ for $2 \le t \le 4$.
(i)[3]
Find the greatest velocity attained by $P$ during the first $2\text{ s}$.
(ii)[2]
Determine, with justification, whether $P$ has any instantaneous change in acceleration when $t = 2$.
(iii)[3]
Sketch the velocity-time graph for $0 \le t \le 4$.
(iv)[5]
Find the distance travelled by $P$ over $0 \le t \le 4$.
Worked solution & mark scheme
This 13-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Differentiate $12t - 4t^2$, giving $\dfrac{dv}{dt} = 12 - 8t$” …