A particle is acted upon by a force `F` which varies with position `x` is shown in figure .If the particle at `x = 0` kinetic energy of `25J` then the kinetic energy of the particle at `x = 16 m` is

Options

A. `45 J`
B. `30 J`
C. `70 J`
D. `20 J`

Answer

A

Explanation

Work done W=Area under F-x graph with proper sign
W=Area of triangle `ABC+` Area of rectangle `C DEF+` Area of rectangle `FGHI+` Area of rectangle `IJKL`
`W=[(1)/(2) xx6xx1-0]+[4xx(-5)]+[4xx(5)]+[2xx(-5)]`
`=30-20-+20-10` (i)
`=20 J`
According to work energy theorem
`K_(f)-K_(i)=W`
or `(K_(f))_(x=16m-(K_(i))_(x=0m)=W`
`(K_(f))_(x=16)m=(K_(i))_(x=0m)+W`
`=25 J+20J` (Usubg (ii))
`=45 J`.