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.

Explanation

`V=Ksqrts`
`(ds)/(dt)=KsqrtS therefore int_0^S (dS)/sqrtS=int_0^t K dt`
`therefore 2sqrtS=Kt` and `S=1/4K^2t^2`
`rArr V=(dS)/(dt)=1/4 K^2 2t=1/2 K^2t`
`therefore V prop t`
`therefore` The V-t graph is a straight line passing through the origin.