Mathematics 9709 · AS & A Level · Kinematics of motion in a straight line
Kinematics of motion in a straight line — practice question
A particle travels along a straight line and passes through point $A$ at time $t = 0$. After leaving $A$, the particle’s velocity at time $t$ s is $v\,\text{m s}^{-1}$, where $v = 2t^2 - 5t + 3$.
(a)[4]
Find the times at which the particle is instantaneously at rest. Hence or otherwise find the minimum velocity of the particle.
(b)[3]
Sketch the velocity-time graph for the first $3$ seconds of motion.
(c)[3]
Find the distance travelled over the interval between the two times when the particle is instantaneously at rest.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Solve $v = 0$, for example by factorising $(2t - 3)(t - 1) = 0$” …