Mathematics 9709 · AS & A Level · Kinematics of motion in a straight line
Kinematics of motion in a straight line — practice question
A particle $P$ travels along a straight line and passes through point $A$ at time $t = 0$. The velocity $v\,\text{m s}^{-1}$ of $P$ at time $t$ seconds is defined by $v = (2t + 1)^{\frac{3}{2}} - 2t^2$, where $0 \le t \le 3$.
(a)[5]
Determine the maximum velocity of $P$ for $0 \le t \le 3$.
(b)[4]
It is stated that, throughout the interval $0 \leq t \leq 3$, the velocity of $P$ remains positive. Find the distance of $P$ from $A$ at the instant when $P$ is travelling at this maximum velocity.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Differentiate $v=(2t+1)^{\frac{3}{2}}-2t^2$.” …