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

Kinematics of motion in a straight line — practice question

An athlete moves along a straight horizontal road. The athlete begins from rest and accelerates at $0.5\text{ m s}^{-2}$ until reaching a speed of $V\text{ m s}^{-1}$. The athlete then keeps this speed of $V\text{ m s}^{-1}$ for $T\text{ s}$ before slowing at $0.2\text{ m s}^{-2}$ until coming to rest. In total, the athlete travels $1350\text{ m}$ in $246\text{ s}$.
(a)[1]

Sketch the velocity-time graph for the athlete’s motion.

(b)[4]

Find $T$ in terms of $V$, and hence show that $7V^2 - 492V + 2700 = 0$.

(c)[2]

Find the value of $V$, and justify your answer.

Worked solution & mark scheme

This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: Accurate velocity-time graph (trapezium beginning and ending on horizontal axis)

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