Mathematics 9709 · AS & A Level · Kinematics of motion in a straight line
Kinematics of motion in a straight line — practice question
Particle $P$ travels along a straight line. It begins at point $O$ on the line and, $t\,\text{s}$ after leaving $O$, its velocity is $v\,\text{m s}^{-1}$, where $v = 6t^2 - 30t + 24$.
(i)[2]
Find the range of values of $t$ for which the particle’s acceleration is negative.
(ii)[4]
Find the distance between the two positions where $P$ is at instantaneous rest.
(iii)[3]
Find the two positive values of $t$ for which $P$ passes through $O$.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Differentiate $v$ to obtain $a = 12t - 30$” …