(i)[2]
Show that this gives $v\frac{dv}{dx} = 5e^{-x} - 3x^2$.
(ii)[5]
As $P$ passes through $O$, its velocity is $6\,\text{m s}^{-1}$. Find the velocity of $P$ when $x = 2$.
Mathematics 9709 · AS & A Level · Probability
Probability — practice question
A particle $P$ with mass $0.8\,\text{kg}$ travels along the $x$-axis on a horizontal surface. If the displacement of $P$ from the origin $O$ is $x\,\text{m}$, then its velocity is $v\,\text{m s}^{-1}$ in the positive $x$-direction. Two horizontal forces act on $P$. One has magnitude $4e^{-x}\,\text{N}$ and acts in the positive $x$-direction. The other has magnitude $2.4x^2\,\text{N}$ and acts in the negative $x$-direction.