A particle is moving on a linear pathway whose acceleration varies as a=2x(where, x is its distance covered) If it had started from rest(zero velocity when x=0),find an equation to suggest its velocity-displacement relationship? How to solve? Pls help

1 Answer
Mar 5, 2018

As the particle is moving in a linear pathway,we can say its distance covered will be equals to displacement,also because it only accelerates.

We know,accleration = rate of change in velocity = (dv)/(dt)

So,we can write, (dv)/(dt) =2x

or, (dv)/(dx) (dx)/(dt) =v(dv)/(dx)=2x (as, velocity = rate of change in velocity)

So,we can write,

vdv =2xdx

or, int_0^V vdv =2 int_0^x xdx (as, at x=0,v=0)

so, V^2/2 = 2 (x^2/2)=x^2

or, V^2 =2x^2

or, V=sqrt(2) x

this is the required velocity displacement relationship.