Mathematics 9709 · AS & A Level · Kinematics of motion in a straight line
Kinematics of motion in a straight line — practice question
A particle $P$ leaves rest from a point $O$ on a straight line and travels along that line. Its displacement after $t\,\text{s}$ from leaving $O$ is $x = 0.08t^2 - 0.0002t^3$.
(i)[4]
Find the value of $t$ when $P$ gets back to $O$ and find the speed of $P$ as it goes through $O$ on the return journey.
(ii(a))[3]
For the motion of $P$ up to the instant it comes back to $O$, find the total distance travelled.
(ii(b))[2]
For the motion of $P$ up to the instant it returns to $O$, find the average speed.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Time taken is $\dfrac{0.08}{0.0002}=400\,\text{s}$” …