Physics-
General
Easy

Question

The given graph shows the variation of velocity with displacement. Which one of the graph given below correctly represents the variation of acceleration with displacement

  1.    
  2.    
  3.    
  4.    

The correct answer is:


    Given line have positive intercept but negative slope. So its equation can be written as
    v equals negative m x plus v subscript 0 end subscript…..(i)[where m equals tan invisible function application theta equals fraction numerator v subscript 0 end subscript over denominator x subscript 0 end subscript end fraction]
    By differentiating with respect to time we get fraction numerator d v over denominator d t end fraction equals negative m fraction numerator d x over denominator d t end fraction equals negative m v
    Now substituting the value of v from eq. (i) we get fraction numerator d v over denominator d t end fraction equals negative m left square bracket negative m x plus v subscript 0 end subscript right square bracket equals m to the power of 2 end exponent x minus m v subscript 0 end subscript \ a equals m to the power of 2 end exponent x minus m v subscript 0 end subscript
    i.e. the graph between a and x should have positive slope but negative intercept on a-axis. So graph (a) is correct

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