(a)[4]
Find the particle's displacement from $O$ when $t = 1$.
(b)[7]
Show that the particle's minimum velocity is $-125\,\text{m s}^{-1}$.
Mathematics 9709 · AS & A Level · Kinematics of motion in a straight line
Kinematics of motion in a straight line — practice question
A particle travels along a straight line. It begins from rest at a fixed point $O$ on the line. At time $t\text{ s}$ after leaving $O$, its velocity is $v\text{ m s}^{-1}$, where $v = t^2 - 8t^{\frac{3}{2}} + 10t$.
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This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: “By integrating $v$, $s=\int(t^2-8t^{\frac{3}{2}}+10t)\,dt$” …
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