(i)[4]
Find a formula for the displacement of $P$ from $O$ as a function of $t$.
(ii)[3]
Hence find how long $P$ takes to get back to point $O$.
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. $t$ seconds after it starts from rest at the point $O$ on the line, its acceleration is $a\,\text{m s}^{-2}$, where $a = 0.075t^{2} - 1.5t + 5$.