A particle located at x = 0 at time t = 0, starts moving along the positive x - direction with a velocity `'upsilon'` that varies as `upsilon=alpha sqrt(x)`. The displacement of the particle varies with time as

Options

A. ` t^(1//2)`
B. ` t^(3)`
C. ` t^(2) `
D. t

Answer

C

Explanation

we are given ` v= alpha sqrt x " "v =(dx)/(dt) alpha sqrt x or (dx)/(sqrt x) =alpha dt `
int _0^(x) (dx)/(sqrtx) =alpha int _0^(t) dt = alpha " "or " " 2x ^(1//2) =alpha t " "or " " x=((alpha )/(2))^(2) t^(2) or " " ` displacement is proportional to `t^(2) `