A man running with a uniform speed 'u' on a straight road observes a stationary bus at a distance 'd' ahead of him. At that instant, the bus starts with an acceleration 'a'. The condition that he would be able to catch the bus is?

Asked by adityaahuja099 | 11th Oct, 2017, 07:16: PM

Expert Answer:

 begin mathsize 12px style The space velocity space of space the space bus space after space time space straight t space space is space straight v equals at space
When space the space man space reaches space bus space he space will space have space more space velocity space than space the space bus space space straight u greater than at space
space therefore space space straight t less than straight u over straight a end style
 begin mathsize 12px style Distance space traveled space by space the space man space in space time space straight t space straight i. straight e. space left parenthesis ut right parenthesis space is space
space the space sum space of space the space distance space between space him space space and space space the space bus space at space that space instant space left parenthesis straight d right parenthesis space and space
space distance space covered space by space the space bus space after space its space starts space accelerating space left parenthesis 1 half gt squared right parenthesis end style 
  begin mathsize 12px style ut equals straight d plus 1 half at squared
straight d equals ut minus 1 half at squared
straight d less or equal than ux straight u over straight a minus 1 half xax straight u squared over straight a squared
straight d less or equal than fraction numerator straight u squared over denominator 2 straight a end fraction end style

This is the condition for the man to catch the bus

Answered by Gajendra | 29th Nov, 2017, 02:49: PM