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. Its velocity $v\,\text{m s}^{-1}$ at time $t\,\text{s}$ is defined by
$v = 5t(t - 2)$ for $0 \leq t \leq 4$,
$v = k$ for $4 \leq t \leq 14$,
$v = 68 - 2t$ for $14 \leq t \leq 20$, where $k$ is constant.
(i)[1]
Find the value of $k$.
(ii)[3]
Sketch the velocity-time graph for $0 \leq t \leq 20$.
(iii)[2]
Find the set of values of $t$ for which the acceleration of $P$ is positive.
(iv)[5]
Find the total distance travelled by $P$ over the interval $0 \leq t \leq 20$.
Worked solution & mark scheme
This 11-mark question has a full step-by-step worked solution and mark scheme.