A particle starts from rest and moves with an acceleration of `a={2+|t-2|}m//s^(2)` The velocity of the particle at `t=4` sec is

Options

A. ` 16 m//s`
B. ` 20 m//s`
C. ` 8m//s `
D. ` 12 m//s`

Answer

D

Explanation

` {:(4-t, ,0lttle2),(t, ,2letle4):} t=0 "to" sec : (dv)/(dt) =4-t " "rArr " "int _0^(v) dv =int _0^(2) (4-t)dt `
` v=[4t-t^(2)//2) ]_0^(2) =6m//s ` velocity at (t=2 sec ).=6m//s
` underset_(t=2"to" 4 sec ):(dv)/(dt) =t rArr int _6^(v) dv =int _2^(4) tdt rArr v= 6 +6=12m //s `