(i)[2]
Show that the equation becomes $v\frac{dv}{dx} = 5 - 2e^{-x}$.
(ii)[4]
Find the value of $v$ when $x = 0.6$.
Mathematics 9709 · AS & A Level · Representation of data
Representation of data — practice question
A particle $P$ with mass $0.4\,\text{kg}$ is let go from rest at point $O$ on a smooth plane inclined at $30^\circ$ to the horizontal. If the displacement of $P$ from $O$ is $x\,\text{m}$ down the plane, then its velocity is $v\,\text{m s}^{-1}$. A force of magnitude $0.8e^{-x}\,\text{N}$ acts on $P$ up the plane along the line of greatest slope through $O$.