(i)[2]
Show that the relation is $v\frac{dv}{dx} = 10 - 0.03x^2$.
(ii)[1]
Find the value of $x$ when the velocity of $P$ is greatest.
(iii)[4]
Calculate the greatest value of $v$.
Mathematics 9709 · AS & A Level · Representation of data
Representation of data — practice question
A particle $P$ with mass $0.5\,\text{kg}$ is let go from rest at point $O$ and moves straight down. After it has descended a distance of $x\,\text{m}$ from $O$, its speed is $v\,\text{m s}^{-1}$. A resisting force of magnitude $0.015x^2\,\text{N}$ acts on $P$.
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This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Forms the equation of motion $0.5v\,dv/dx = 0.5g - 0.015x^2$” …
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