A body is moves along a straight line by a machine dellvering a constant power . The distance moved by the body in time `t` is propertional as

Options

A. `t^(3//4)`
B. `t^(3//2)`
C. `t^(1//4)`
D. `t^(1//2)`

Answer

B

Explanation

We get that `F xx nu = poewr
`:. M(dnu)/(dt) xx nu = c ( :. F = ma = (mdnu)/(dt)) `
` m int_(0) ^(v) nu d nu = c int _(0)^(t) dt :. (1)/(2) mnu^(2) = ct `
`:. Nu = sqrt(2c)/(m) xx t^(1/2) ` where `nu = (dx)/(dt) `
`:. Int _(0)^(x) dx = sqrt(2c)/(m)) xx int _(0) ^(t) t^(1/2) dt `
`x = sqrt(2c)/(0m) xx (2t^(3/2))/(3) rArr x prop t^(3/2) ` .