(i)[2]
Show that, after simplification, $v\frac{dv}{dx} = 10 - 0.5v^2$.
(ii)[4]
Express $v$ as a function of $x$.
(iii)[2]
Find the increase in the value of $v$ over the final $4\,\text{m}$ of the object’s descent.
Mathematics 9709 · AS & A Level · Probability
Probability — practice question
An object of mass $0.4\,\text{kg}$ is dropped from rest from a point $8\,\text{m}$ above the ground. It falls vertically, and when its downward displacement from the starting position is $x\,\text{m}$ the speed is $v\,\text{m s}^{-1}$. As the object moves, a force of magnitude $0.2v^2\,\text{N}$ acts opposite to the motion.
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This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Applies Newton’s Second Law vertically: $0.4a = 0.4g - 0.2v^2$” …
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