Mathematics 9709 · AS & A Level · Kinematics of motion in a straight line
Kinematics of motion in a straight line — practice question
A particle leaves point $O$ and travels along a straight line. The velocity of the particle at time $t\,\text{s}$ after leaving $O$ is $v\,\text{m s}^{-1}$, where $v = 1.5 + 0.4t$ for $0 \leq t \leq 5$, and $v = \frac{100}{t^2} - 0.1t$ for $t \geq 5$.
(i)[1]
Find the acceleration of the particle over the first $5$ seconds of motion.
(ii)[2]
Find the value of $t$ for which the particle is instantaneously at rest.
(iii)[5]
Find the total distance covered by the particle in the first $10$ seconds of motion.
(c)[5]
Find the total distance covered by the particle in the first $10$ seconds of motion.
Worked solution & mark scheme
This 13-mark question has a full step-by-step worked solution and mark scheme. One marking point: “State the acceleration to be $0.4\,\text{m s}^{-2}$” …