Mathematics 9709 · AS & A Level · Kinematics of motion in a straight line

Kinematics of motion in a straight line — practice question

A particle $X$ travels along a straight line. Its displacement from $O$ at time $t$ after leaving $O$ is $s\,\text{m}$, where $s = 0.3t^2 + 0.6t$ for $0 \le t \le 4$. For $t > 4$, the acceleration of $X$ at time $t$ after leaving $O$ is $a\,\text{m s}^{-2}$, where $a = 0.3t^{\frac{1}{2}}$. The velocity of $X$ does not change at $t = 4$. The velocity of $X$ at $t = T$ is $14.2\,\text{m s}^{-1}$.
(a)[2]

Find the velocity of $X$ when $t = 4$.

(b(i))[4]

Find $T$.

(b(ii))[4]

Find the total distance travelled by $X$ from $t = 0$ to $t = T$.

Worked solution & mark scheme

This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: Velocity given by $v=0.6t+0.6$

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