Physics-
General
Easy

Question

A man is 45 blank m behind the bus when the bus start accelerating from rest with acceleration 2.5 blank m divided by s to the power of 2 end exponent. With what minimum velocity should the man start running to catch the bus

  1. 12 blank m divided by s  
  2. 14 blank m divided by s  
  3. 15 blank m divided by s  
  4. 16 blank m divided by s  

The correct answer is: 15 blank m divided by s


    Let man will catch the bus after ‘ts e c. So he will cover distance u t
    Similarly distance travelled by the bus will be fraction numerator 1 over denominator 2 end fraction a t to the power of 2 end exponent
    For the given condition
    u blank t equals 45 plus fraction numerator 1 over denominator 2 end fraction a blank t to the power of 2 end exponent equals 45 plus 1.25 t to the power of 2 end exponent blank left square bracket A s blank a equals 2.5 blank m divided by s to the power of 2 end exponent right square bracket
    rightwards double arrow u equals fraction numerator 45 over denominator t end fraction plus 1.25 t
    To find the minimum value of u
    fraction numerator d u over denominator d t end fraction equals 0 sp we get t equals 6 blank s e c then,
    u equals fraction numerator 45 over denominator 6 end fraction plus 1.25 cross times 6 equals 7.5 plus 7.5 equals 15 blank m divided by s

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