Mathematics 9709 · AS & A Level · Kinematics of motion in a straight line
Kinematics of motion in a straight line — practice question
A particle $X$ moves along a straight line. Let its velocity at time $t$ s after departing from a fixed point $O$ be $v\text{ m s}^{-1}$, where $v = -0.1t^3 + 1.8t^2 - 6t + 5.6$. The acceleration of $X$ is zero when $t = p$ and when $t = q$, with $p < q$.
(a)[4]
Determine the value of $p$ and the value of $q$.
(b)[3]
It is given that the velocity of $X$ is zero at $t = 14$. Determine the velocities of $X$ at $t = p$ and at $t = q$, and then sketch the velocity-time graph for the motion of $X$ for $0 \leq t \leq 15$.
(c)[5]
Determine the total distance travelled by $X$ from $t = 0$ to $t = 15$.
Worked solution & mark scheme
This 12-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Differentiate $v$ with the powers altered correctly” …