Physics-
General
Easy

Question

A car moves from X blank t o blank Y with a uniform speed v subscript u end subscript and returns to Y with a uniform speed v subscript d end subscript. blankThe average speed for this round trip is

  1. fraction numerator 2 v subscript d end subscript v subscript u end subscript over denominator v subscript d end subscript plus v subscript u end subscript end fraction  
  2. square root of v subscript u end subscript v subscript d end subscript end root  
  3. fraction numerator v subscript d end subscript v subscript u end subscript over denominator v subscript d end subscript plus v subscript u end subscript end fraction  
  4. fraction numerator v subscript u end subscript plus v subscript d end subscript over denominator 2 end fraction  

The correct answer is: fraction numerator 2 v subscript d end subscript v subscript u end subscript over denominator v subscript d end subscript plus v subscript u end subscript end fraction


    Let t subscript 1 end subscript blank a n d blank t subscript 2 end subscript be times taken by the car to go from X blank t o blank Y and then from Y blank t o blank X respectively.
    Then, t subscript 1 end subscript plus t subscript 2 end subscript equals fraction numerator X Y over denominator v subscript u end subscript end fraction plus fraction numerator X Y over denominator v subscript d end subscript end fraction equals X Y blank open parentheses fraction numerator v subscript u end subscript plus u subscript d end subscript over denominator v subscript u end subscript v subscript d end subscript end fraction close parentheses
    Total distance travelled
    blank equals X Y plus X Y equals 2 blank X Y
    Therefore, average speed of the car for this round trip is
    A v e r a g e blank s p e e d equals fraction numerator d i s t a n c e blank t r a v e l l e d over denominator t i m e blank t a k e n end fraction
    v subscript a v end subscript equals fraction numerator 2 blank X Y over denominator X Y blank open parentheses fraction numerator v subscript u end subscript plus v subscript d end subscript over denominator v subscript u end subscript v subscript d end subscript end fraction close parentheses end fraction o r blank v subscript a v end subscript equals fraction numerator 2 v subscript u end subscript v subscript d end subscript over denominator v subscript u end subscript plus v subscript d end subscript end fraction

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