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 through point $O$. Its displacement from $O$ at time $t$ is $s\,\text{m}$, where $s = t^2 - 3t + 2$ for $0 \le t \le 6$, and $s = \frac{24}{t} - \frac{t^2}{4} + 25$ for $t > 6$.
(a)[2]
Determine the value of $t$ when the particle is instantaneously at rest in the first $6$ seconds of its motion.
(b)[3]
At $t = 6$, the particle strikes a barrier at point $P$ and rebounds. Determine the velocity at which the particle reaches $P$ and the velocity at which it departs from $P$.
(c)[5]
Determine the total distance travelled by the particle in the first $10$ seconds of its motion.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Differentiate $s$ to get $v = 2t - 3$ for $0 \le t \le 6$” …