The correct option is D 4 m/s
As we know that,
dvdt=a
⇒ ∫dv=∫a dt
Since, a=(t−2), has negative value for t<2 and positive value for t>2, so, the value of function a=|t−2| will be
a=−(t−2);t<2
and a=(t−2);t>2
⇒ ∫v0v dv=∫20−(t−2)dt+∫42(t−2)dt
⇒ v=[−t22+2t]20+[t22−2t]42
⇒ v=2+2=4 m/s