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A body of mass m moving along a straight line covers half the distance with a speed of 2 m s to the power of negative 1 end exponent. The remaining half of distance is covered in two equal time intervals with a speed of 3 blank m s to the power of negative 1 end exponent a n d blank 5 blank m s to the power of negative 1 end exponent respectively. The average speed of the particle for the entire journey is

  1. fraction numerator 3 over denominator 8 end fraction m s to the power of negative 1 end exponent  
  2. fraction numerator 8 over denominator 3 end fraction m s to the power of negative 1 end exponent  
  3. fraction numerator 4 over denominator 3 end fraction m s to the power of negative 1 end exponent  
  4. fraction numerator 16 over denominator 3 end fraction m s to the power of negative 1 end exponent  

The correct answer is: fraction numerator 8 over denominator 3 end fraction m s to the power of negative 1 end exponent


    Let the total distance travelled by the body is 2 S. If t subscript 1 end subscript is the time taken by the body to travel first half of the distance, then
    blank t subscript 1 end subscript equals fraction numerator S over denominator 2 end fraction
    Let t subscript 2 end subscript be the time taken by the body for each time interval for the remaining half journey.
    therefore blank S equals 3 t subscript 2 end subscript plus 5 t subscript 2 end subscript equals 8 t subscript 2 end subscript
    S o comma blank a v e r a g e blank s p e e d blank equals fraction numerator T o t a l blank d i s t a n c e blank t r a v e l l e d over denominator T o t a l blank t i m e blank t a k e n end fraction
    blank equals fraction numerator 2 S over denominator t subscript 1 end subscript plus 2 t subscript 2 end subscript end fraction equals fraction numerator 2 S over denominator fraction numerator S over denominator 2 end fraction plus fraction numerator S over denominator 4 end fraction end fraction equals fraction numerator 8 over denominator 3 end fraction m s to the power of negative 1 end exponent

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