(i)[5]
Show that $k = 0.1$.
(ii)[2]
Find an expression for the particle’s displacement from the origin in terms of $t$.
(iii)[1]
Hence verify that the particle is once more at the origin at $t = 2$.
Mathematics 9709 · AS & A Level · Kinematics of motion in a straight line
Kinematics of motion in a straight line — practice question
A particle is released from a fixed origin with velocity $0.4\,\text{m s}^{-1}$ and travels along a straight line. After $t$ seconds, the acceleration $a\,\text{m s}^{-2}$ is given by $a = k(3t^2 - 12t + 2)$, where $k$ is constant. At $t = 1$, the velocity of $P$ is $0.1\,\text{m s}^{-1}$.
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This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “$v = k(3t^2 - 12t + 2)$, obtained by applying $v = \int a\,dt$” …
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