Mathematics 9709 · AS & A Level · Kinematics of motion in a straight line

Kinematics of motion in a straight line — practice question

The diagram is a velocity-time graph that represents the motion of a particle. It is made up of three straight-line sections. The particle’s velocity at time $t$ after passing a fixed point $O$ is $v\,\text{m s}^{-1}$. It leaves $O$ with speed $5\,\text{m s}^{-1}$ and accelerates at $0.75\,\text{m s}^{-2}$ for $20\,\text{s}$. It then decelerates over the next $30\,\text{s}$. When $t = 40$, the particle’s velocity is zero. After $t = 40$, it turns back towards $O$ and comes to rest at $O$ at time $T\,\text{s}$.
(a)[5]

Calculate $T$.

(b)[2]

Calculate the acceleration of the particle from $t = 50$ to $t = T$.

Worked solution & mark scheme

This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: Velocity at $t=20$ equals $5+\tfrac34\times20=20\text{ m s}^{-1}$

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