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

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

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

The velocity of a particle moving in the positive direction of the x axis varies as v= a*sqrt(x)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?