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=K sqrts`
`(d S)/(dt)=K sqrtS" "therefore underset(0)overset(s)int (d S)/sqrtS =underset(0)overset(t)int K dt`
`2sqrtS=Kt and S=1/4 K^(2) t^(2)`
`rArr V=(d S)/(dt)=1/4 K^(2)2t+1/2 K^(2)t`

`therefore V alpha t`
The V-t graph is a straight line passing through the origin.