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

Kinematics of motion in a straight line — practice question

A car sets off from rest and travels in a straight line from point $A$ with constant acceleration $3\text{ m s}^{-2}$ for $10\text{ s}$. It then moves at a constant speed for $30\text{ s}$ before slowing down uniformly and stopping at point $B$. The distance $AB$ is $1.5\text{ km}$.
(i)[3]

Determine the total distance covered during the first $40\text{ s}$ of the motion.

(ii)[6]

Once the car has been moving for $20\text{ s}$, a motorcycle begins from rest and speeds up uniformly in a straight line from point $A$ to a speed $V\text{ m s}^{-1}$. It then keeps this speed for $30\text{ s}$ before slowing uniformly to rest at point $B$. The motorcycle stops at the same instant as the car. Given that the size of the acceleration $a\text{ m s}^{-2}$ of the motorcycle is three times the size of its deceleration, find the value of $a$.

(iii)[3]

Draw the displacement-time graph for the car’s motion.

Worked solution & mark scheme

This 12-mark question has a full step-by-step worked solution and mark scheme. One marking point: $v$ is $3 \times 10 = 30\text{ m s}^{-1}$

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