A wheel which initiallty at rest starts rotating at time `t = 0`. The angular acceleration `prop` decrease from `50 rad//s^2` to zero value `5` seconds. During this interval, `prop` varies according to the.
`prop = prop_0(1 - (t)/(5))`
The angular velocity of the wheel at `t = 5 s` will be.

Options

A. `10 rad//s`
B. `250 rad//s`
C. `125 rad//s`
D. `100 rad//s`

Answer

C

Explanation

( c) Given `prop = prop_0 (1 - (t)/(5))`
`prop = (d omega)/(dt) = prop_0 (1 - (t)/(5))`
:. `int_0^(omega) d omega - prop_0 int_0^5(1 - (t)/(5)) dt rArr omega = prop_0[t - (t^2)/(10)]_0^5`
=`50(5 - (25)/(10))rad//s = 125 rad//s`.