A truck accelerates from speed v to 2v. Work done in during this is

Options

A. three times as the work done in accelerating it from rest to v
B. same as the work dine in accelerating it from rest to v
C. four times as the work done in accelerating it from rest to v
D. less than the work done in accelerating it from rest to v

Answer

A

Explanation

(a) Work done to accelerate from 0 to v is, `W_(1)=(1)/(2)mv^(2)`
Work done to accelerate from v to 2v is, `W_(2)=(1)/(2)m(2v)^(2)`
`rArrDeltaW=W_(2)-W_(1)=(1)/(2)m(2v)^(2)-(1)/(2)mv^(2)=4W_(1)-W_(1)=3W_(1)`