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

Kinematics of motion in a straight line — practice question

A car moves on a straight road with constant acceleration $a\,\mathrm{m\,s^{-2}}$, where $a>0$. The car goes through the points $A$, $B$ and $C$ in that order. At $A$, the car has speed $u\,\mathrm{m\,s^{-1}}$ in the direction $AB$. The distance $BC$ is twice the distance $AB$. The car takes $8$ seconds to go from $A$ to $B$ and $10$ seconds to go from $B$ to $C$.
(a)[4]

Find $u$ as a function of $a$.

(b)[2]

Find the car's speed at $C$ in terms of $a$.

Worked solution & mark scheme

This 6-mark question has a full step-by-step worked solution and mark scheme. One marking point: Apply SUVAT formulae to write distance expressions for AB, BC or AC, for example $s=ut+\tfrac12at^2$ or $s=\tfrac{u+v}{2}t$

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