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.
Worked solution & mark scheme
This 6-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Accurate trapezium shape with the right-hand gradient steeper than the left-hand gradient” …