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 CDEF+Area of rectangle FGHI+Area of rectangle IJKL
`W=[1/2xx6xx10]+[4xx(-5)]+[4xx(5)]+[2xx(-5)]`
=30-20+20-10= 20 J...(i)
According to work energy theorem
`K_f-K_i=W`
or `(K_f)_(x=16m) - (K_i)_(x=0 m)=W`
`(K_f)_(x=16m) = (K_i)_(x=0 m)+W`=25 J + 20 J =45 J