question_answer

A body travels with velocity \[{{\upsilon }_{1}}\] for time \[{{t}_{1}}\] second and with velocity\[{{\upsilon  }_{2}}\]  for time \[{{t}_{2}}\] second in the same       direction, find the average velocity of the body.                

Answer:

                Since, the particles while moving with constant speed \[\upsilon \], are always at a constant distance d, they must be at the two ends of the diameter of a circular path. The diameter of this circular path = d. Each particle will return to its initial position after describing a circular path = \[2\pi r=\pi d\]                                                         (\[\because \,\,2r=d\]) Time interval after which each particle will return to its initial position = distance travelled/speed = \[\pi \,d/\upsilon \]