The angle of rotation of a particle is given as a function of time as `theta = theta_(1) + at + bt^(2)` where `theta_(0)` is initial angular displacement and a and b are constants. If the initial angular velocity is `3 pi` radians per second and after 2 sec angulare velocity is `8 pi` radians per second, then a and b respectively in SI unit are:

Options

A. `3 pi, 3pi`
B. `3pi, 1.25 pi`
C. `1.2pi, 3pi`
D. `1.25 pi, 1.25 pi`

Answer

B

Explanation

`omega = (d theta)/(dt) = a + 2bt`
`3 pi = a + 2b xx 0`
`8 pi = a + 4b`
Solving above, we get a and b.