(i)[5]
Determine the total time taken by the cyclist to go from A to B.
(ii)[5]
Determine the time from when the cyclist leaves until the car overtakes her.
Mathematics 9709 · AS & A Level · Kinematics of motion in a straight line
Kinematics of motion in a straight line — practice question
A cyclist leaves point A from rest and travels in a straight line with acceleration $0.5\,\text{m s}^{-2}$ over a distance of $36\,\text{m}$. The cyclist then continues at constant speed for $25\,\text{s}$ before decelerating uniformly until coming to rest at point B. The distance $AB$ is $210\,\text{m}$. $24\,\text{s}$ after the cyclist leaves point A, a car sets off from rest from point A, with constant acceleration $4\,\text{m s}^{-2}$, towards B. It is given that the car overtakes the cyclist while the cyclist is moving with constant speed.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Applying $s = ut + \tfrac12 at^2$, for example $36 = 0 + 0.5 \times 0.5t^2$, so $t = 12$” …
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