The velocity of a particle moving in the positive direction of the x axis varies as v= a*#sqrt(x)#, where a is a positive constant. Assuming that at the moment t = 0 the particle was located at the point x = 0, find the time dependence of the velocity?

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Answer 1 · 2017-08-28T16:06:53

Given relation between velocity (#v#) and displacement (#x#) is

#v=asqrtx#

#=>(dx)/(dt)=asqrtx#

#=>(dx)/sqrtx=adt#

#=>int(dx)/sqrtx=aintdt#

#=>x^(-1/2+1)/(-1/2+1)=at+c#

Since at #t=0# #x=0#

we get #c=0#

So #2sqrtx=at#

#=>4x=a^2t^2#

#=>x=1/4a^2*t^2#

Differentiating w r to t we get

#v=(dx)/(dt)=1/4a^2(2t^(2-1))#

#=>v=1/2(a^2t)#