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

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Answer 1 · 2018-03-05T15:07:08

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.