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 rest at point $O$ and travels along a horizontal straight line. At time $t\text{ s}$ after leaving $O$, its velocity is $v\text{ m s}^{-1}$. When $0 \le t < 60$, the velocity is given by $v = 0.05t - 0.0005t^2$. At $t = 60$, the particle strikes a wall and then changes the direction of its motion. It later comes to rest at point $A$ when $t = 100$, and for $60 < t \le 100$ the velocity is given by $v = 0.025t - 2.5$.
(i)[2]
Find the velocity of the particle just before it hits the wall, and the velocity of the particle just after it hits the wall.
(ii)[4]
Find the particle’s total distance travelled.
(iii)[4]
Find the particle’s maximum speed and sketch the velocity-time graph for the particle for $0 \le t \le 100$, indicating the value of $t$ for which the speed is greatest.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Immediately before impact, the velocity is $1.2\,\text{m s}^{-1}$” …