# A body is in rectilinear motion with a acceleration given by a=2v​3/2. If the particle starts its motion fro origin with velocity of 4m/s, the position x of the particle at an instant terms of v can be given as

Dear Student,

$a=2{v}^{3}{2}}\phantom{\rule{0ex}{0ex}}\frac{vdv}{dx}=2{v}^{3}{2}}\phantom{\rule{0ex}{0ex}}dx=\frac{vdv}{2{v}^{3}{2}}}\phantom{\rule{0ex}{0ex}}{\int }_{0}^{x}dx={\int }_{4}^{v}\frac{dv}{2\sqrt{v}}\phantom{\rule{0ex}{0ex}}x={\left|\sqrt{v}\right|}_{4}^{v}\phantom{\rule{0ex}{0ex}}x=\sqrt{v}-2\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}Regards\phantom{\rule{0ex}{0ex}}$

• -1
What are you looking for?