A body is moved along a straight line by a machine delivering constant power . The distance moved by the body is time `t` is proptional to

Options

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

Answer

D

Explanation

Power , P = Force `xx` Velocity
= `F xx v`
`=ma xx v` = constant
So , va = constant
`v""(dv)/(dt)` = constant
Integrating it , we have
`(v^(2))/(2) = Ct`
or ` v = sqrt(2CT) = C_(1) t^(1//2)`
or `(dx)/(dt) = C_(1)t^(1//2)`
Integrating it , we get
`x = C_2 t^(3//2)`
So , `x prop t^3//2 `