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

Kinematics of motion in a straight line — practice question

A train runs between stations $A$ and $B$. It leaves $A$ from rest and increases its speed at a constant rate for $T\,\text{s}$ until its speed becomes $25\,\text{m\,s}^{-1}$. It then continues at this same speed before slowing down at a constant rate and stopping at $B$. The size of the train’s deceleration is twice the size of its acceleration. The whole trip takes $180\,\text{s}$.
(i)[1]

Sketch the velocity-time graph for the train’s trip from $A$ to $B$.

(ii)[2]

Find an expression, in terms of $T$, for the duration of the interval when the train is moving at constant speed.

(iii)[3]

The distance from $A$ to $B$ is $3300\,\text{m}$. Determine how far the train covers while it is decelerating.

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