Physics-
General
Easy

Question

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

  1. 45 blank J    
  2. 30 blank J    
  3. 70 blank J    
  4. 135 blank J    

The correct answer is: 45 blank J


    Work done W equals Area under F-xgraph with proper sign W equals Area of triangle A B C + Area of rectangle C D E F + Area of rectangle F G H I + Area of I J K L

    W equals open square brackets fraction numerator 1 over denominator 2 end fraction blank cross times 6 cross times 10 close square brackets plus open square brackets 4 cross times left parenthesis negative 5 right parenthesis close square brackets plus open square brackets 4 cross times 5 close square brackets plus open square brackets 2 cross times open parentheses negative 5 close parentheses close square brackets
    rightwards double arrow W equals 30 minus 20 plus 20 minus 10 equals 20 blank J ….(i)
    According to work energy theorem
    K subscript f end subscript minus K subscript i end subscript equals W rightwards double arrow open parentheses K subscript f end subscript close parentheses subscript x equals 16 m end subscript minus open parentheses K subscript i end subscript close parentheses subscript x equals 0 m end subscript equals W
    open parentheses K subscript f end subscript close parentheses subscript x equals 16 m end subscript equals open parentheses K subscript i end subscript close parentheses subscript x equals 0 m end subscript plus W
    equals 25 blank J plus 20 blank J equals 45 blank J [Using (i)]

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