A particle of mass 0.1 kg is subjected to a force which varies with distance as shown in figure. If it starts its journey from rest at `x=0`, its velocity at `x=12m` is

Options

A. `0 m//s`
B. `20 sqrt(2) m//s`
C. `20 sqrt(3) m//s`
D. `40 m//s`

Answer

D

Explanation

(d) Area between curve and displacement axis
=`(1)/(2) xx (12 + 4) xx 10 = 80 J`
In this time the body acquired kinetic energy `= (1)/(2) mv^2` by the law of conservation of energy
`(1)/(2) mv^2 = 80 J`
`rArr (1)/(2) xx 0.1 xx v^2 = 80`
`rArr v^2 = 1600`
`rArr v = 40 m//s`.