Mathematics 9709 · AS & A Level · Kinematics of motion in a straight line
Kinematics of motion in a straight line — practice question
A particle begins at rest and travels along a straight line. After $t\,\text{s}$ from the start, its velocity is $v\,\text{m s}^{-1}$, where $v = -0.01t^3 + 0.22t^2 - 0.4t$.
(i)[2]
Find the two positive values of $t$ at which the particle is instantaneously at rest.
(ii)[3]
Find the time when the particle's acceleration is greatest.
(iii)[4]
Find the distance travelled by the particle during the time when its velocity is positive.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Try solving $v = 0$, which leads to a quadratic such as $-0.01(t-20)(t-2)=0$” …