Acceleration of a particle is given by `vec a = (2t +5) hatims^(-2).` Calculate the velocity of particle after 5s, if it starts from rest.

Options

A. `hati (m)/(s)`
B. `50 hati (m)/(s)`
C. `75 hati (m)/(s)`
D. ` 100 hati (m)/(s)`

Answer

B

Explanation

`a = (2t + 5) hati ms ^(-2)`
`therefore (dv)/(dt) = (2t +5) hati ms ^(-2) ( because a = (dv)/(dt))`
`therefore int dv = int _(0) ^(5) (2t + 5) dt`
`therefore v = [ 2 (t ^(2))/( 2 ) + 5t] _(0) ^(5) = 25 + 25 = 50 hat i ms ^(-1)`