(i)[5]
Determine the velocity of the particle when $t = 4$ and when $t = 60$, and sketch the velocity-time graph.
(ii)[2]
Calculate the distance $XY$.
Mathematics 9709 · AS & A Level · Kinematics of motion in a straight line
Kinematics of motion in a straight line — practice question
A particle begins from rest at point $X$ and travels in a straight line. After $60$ seconds, it arrives at point $Y$. For time $t$ seconds after leaving $X$, the acceleration of the particle is $0.75\,\text{m s}^{-2}$ for $0 \le t \le 4$, $0\,\text{m s}^{-2}$ for $4 \le t \le 54$, and $-0.5\,\text{m s}^{-2}$ for $54 \le t \le 60$.