Physics-
General
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Question

A 10 kg brick moves along an x-axis. Its acceleration as a function of its position is shown in figure. What is the net work performed on the brick by the force causing the acceleration as the brick moves from x equals 0 to x equals 8.0m?

  1. 4 J    
  2. 8 J    
  3. 2 J    
  4. 1 J    

The correct answer is: 8 J


    According to the graph the acceleration a varies linearly with the coordinate x. We may write a equals alpha x, where alpha is the slope of the graph.
    From the graph
    alpha equals fraction numerator 20 over denominator 8 end fraction m g subscript 0 end subscript equals 2.5 blank s to the power of negative 2 end exponent
    The force on the brick is in the positive x-direction and according to Newton’s second law, its magnitude is given by
    F equals fraction numerator a over denominator m end fraction equals fraction numerator alpha over denominator m end fraction x
    If x subscript f end subscript is the final coordinate, the work done by the force is
    W equals not stretchy integral from 0 to x subscript f end subscript of F blank d x equals fraction numerator a over denominator m end fraction not stretchy integral subscript 0 end subscript superscript x subscript f end subscript end superscript x blank d x
    equals fraction numerator alpha over denominator 2 m end fraction x subscript f end subscript superscript 2 end superscript equals fraction numerator 2.5 over denominator 2 cross times 10 end fraction cross times open parentheses 8 close parentheses to the power of 2 end exponent
    equals 8 blank J

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