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 particle is acted upon by a force F which varies with position x as

1.	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
Answer» 45 J 30 J 70J 20 J Solution : 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` .