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

Kinematics of motion in a straight line — practice question

The diagram presents a velocity-time graph that describes a car’s motion. It is made up of six straight-line sections. Starting from rest, the car speeds up to $20\,\text{m s}^{-1}$ in $5\,\text{s}$, and then continues at this speed for another $20\,\text{s}$. It next slows to $6\,\text{m s}^{-1}$ in $5\,\text{s}$. That speed is then kept for a further $(T - 30)\,\text{s}$. After that, the car speeds up again to $20\,\text{m s}^{-1}$ over $(50 - T)\,\text{s}$, before slowing to rest in $10\,\text{s}$.
(a)[2]

Given that the accelerations are equal in the two accelerating parts of the motion, find the value of $T$.

(b)[2]

Find the total distance travelled by the car throughout the motion.

Worked solution & mark scheme

This 4-mark question has a full step-by-step worked solution and mark scheme. One marking point: Equate the accelerations and write the equation $\frac{20-6}{50-T}=\frac{20}{5}$ or $20=6+\frac{20}{5}(50-T)$

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