(a)[1]
Determine the speed of the particle for the period from $t = 5$ to $t = 10$.
(b)[2]
Find the acceleration of the particle from $t = 0$ to $t = 5$, assuming it is constant.
(c)[2]
Determine the particle's average speed over the whole motion.
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, with displacement $s$ metres at time $t$ seconds after departing from a fixed point $O$. It starts from rest and is at points $P$, $Q$ and $R$ at times $t = 5$, $t = 10$ and $t = 15$ respectively, then returns to $O$ at time $t = 20$. The distances $OP$, $OQ$ and $OR$ are $50\,\text{m}$, $150\,\text{m}$ and $200\,\text{m}$ respectively. The diagram displays a displacement-time graph representing the particle’s motion from $t = 0$ to $t = 20$. The graph is formed by two curved sections $AB$ and $CD$ and two straight sections $BC$ and $DE$.