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A particle is acted upon by a force F wh...

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

A

45 J

B

30 J

C

70 J

D

20 J

Text Solution

Verified by Experts

The correct Answer is:
A

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
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