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. It begins from rest at a point $O$ on the line. After $t\,\text{s}$ from leaving $O$, the particle’s acceleration $a\,\text{m s}^{-2}$ is defined by $a = 25 - t^2$ for $0 \leq t \leq 9$.
(i)[4]
Find the particle’s maximum velocity during this interval.
(ii)[2]
Find the total distance travelled up to the time when the maximum velocity occurs.
(iii)[4]
For $t > 9$, the acceleration is $a = -3t^{-\frac{1}{2}}$. Find the particle’s velocity when $t = 25$.
(c)[4]
Find the particle’s velocity when $t = 25$.
Worked solution & mark scheme
This 14-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Set the acceleration equal to zero and solve: $25-t^2=0$, so $t=5$” …