(i)[2]
Show that this leads to $v\frac{dv}{dx} = 5e^{-x} - 3x^2$.
(ii)[5]
When $P$ passes through $O$, its velocity is $6\,\text{m s}^{-1}$. Find the velocity of $P$ when $x = 2$.
Mathematics 9709 · AS & A Level · Representation of data
Representation of data — practice question
A particle $P$ with mass $0.8\,\text{kg}$ travels on the $x$-axis over a horizontal plane. If the displacement of $P$ from the origin $O$ is $x\,\text{m}$, 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 is directed in the positive $x$-direction. The other has magnitude $2.4x^2\,\text{N}$ and is directed in the negative $x$-direction.
Worked solution & mark scheme
This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Uses Newton’s Second Law correctly to get $0.8v\dfrac{dv}{dx} = 4e^{-x}-2.4x^2$” …
- Full mark scheme, point by point
- Step-by-step worked solution
- Write your answer & get it marked instantly by AI