Mathematics 9709 · AS & A Level · Representation of data
Representation of data — practice question
A block $B$ of mass $0.25\,\text{kg}$ is released from rest at $O$ on a smooth horizontal surface. Once it has been released, its velocity is $v\,\text{m s}^{-1}$ when its displacement from $O$ is $x\,\text{m}$. The force on $B$ has magnitude $(2 + 0.3x^2)\,\text{N}$ and acts horizontally away from $O$.
(i)[2]
Show that, for this motion, $v\,\frac{dv}{dx} = 1.2x^2 + 8$.
(ii)[3]
Find the velocity of $B$ at $x = 1.5$.
(iii)[2]
A further force acts on $B$ after $x = 1.5$. It is given that, when $x > 1.5$, $v\,\frac{dv}{dx} = 1.2x^2 + 6 - 3x$. Find the magnitude of this extra force and state the direction in which it acts.
Worked solution & mark scheme
This 7-mark question has a full step-by-step worked solution and mark scheme.