Mathematics 9709 · AS & A Level · Kinematics of motion in a straight line
Kinematics of motion in a straight line — practice question
A particle, $P$, moves along a straight path, beginning at point $O$ with velocity $6\,\text{m s}^{-1}$. The acceleration of $P$ at time $t\,\text{s}$ after leaving $O$ is $a\,\text{m s}^{-2}$, where $a = -1.5t^{\frac{1}{2}}$ for $0 \leq t \leq 1$, and $a = 1.5t^{\frac{1}{2}} - 3t^{-\frac{1}{2}}$ for $t > 1$.
(a)[3]
Find the velocity of $P$ at $t = 1$.
(b)[3]
Given that the velocity of $P$ does not change when $t = 1$, find an expression for the velocity of $P$ for $t > 1$.
(c)[4]
Given that the velocity of $P$ is positive for $t \leq 4$, find the total distance travelled between $t = 0$ and $t = 4$.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Attempts integration of $a$ for $0\le t\le1$” …