A truck accelerates from speed v to 2 v. 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 done in acceleating it from rest 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

Let m be mass of the truck.
According to work-energy theorem
`W = K_(f) - K_(i)`
Work done in accelerating the truck from rest to speed v is
`W_(1) = (1)/(2) mv^(2) - 0` (`:'` u = 0)
= `(1)/(2) mv^(2)` …(i)
Work done in accelerating the truck from speed v to 2v is
`W = (1)/(2) m(2v)^(2) - (1)/(2) m(v)^(2)`
= ` (3)/(2) mv(2) = 3(1)/(2) mv^(2) = 3 W_(1)` (Using (i))