Question

A particle $A$ of mass $\frac{10}{7}\text{kg}$ is moving in the positive $x-$ direction. Its initial position is $x=0$ and initial velocity is $1\text{m/s}$. The velocity at $x=10\text{m}$ in $\text{m/s}$ (use the graph given). Answer the nearest integer.

Answer 1

From graph,
$P=0.2x+2=Fv=mav$
or $mv\frac{dv}{dx}v=0.2x+2$
or $m{v}^{2}dv=(0.2x+2)dx$
Now integrate both sides,
$\underset{1}{\overset{v}{\int }}m{v}^{2}dv=\underset{1}{\overset{10}{\int }}(0.2x+2)dx\Rightarrow v=4\text{m/s}$