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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 as shown in figure. If the particle at x * 0 has kinetic energy of 25 J, then the kinetic energy of the particle at x = 16 m is

A

45 J

B

30 J

C

70J

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 = [1/2 xx 6 xx 10] + [4 xx (-5)] + [4 xx (5)] + [2 xx (-5)]`
`= 30 - 20 + 20 - 10 = 20 J`
According to work energy theorem , `K_f - K_i = W`
or `(K_f)_(x = 16m) -(K_i)_(x = 0m) = W`
or `(K_f)_(x = 16m) = (X_i)_(x = 0m) = W = 25J + 20 J = 45J` .
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