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The velocity of a particle moving in the...

The velocity of a particle moving in the positive direction of the X-axis varies as `V = KsqrtS` where K is a positive constant. Draw V-t graph.

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`V=Ksqrt(s)`
`(dS)/(dt)=Ksqrt(S) therefore underset(0)overset(S)int(dS)/(sqrt(S))=underset(0)overset(t)intKdt`
`therefore 2sqrt(S)=Kt and S=(1)/(4)K^(2)t^(2)`
`impliesV=(dS)/(dt)=(1)/(4)K^(2)2t=(1)/(2)K^(2)t`
`therefore Vpropt`
`therefore` The `V-t` graph is a straight line passing through the origin
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