question_answer

The body travels a distance \[{{s}_{1}}\] with velocity \[{{\upsilon }_{1}}\] and \[{{s}_{2}}\] with velocity \[{{\upsilon }_{2}}\] in the same direction. Calculate the average velocity of the body.

Answer:

                Time taken for distance (\[{{s}_{1}}\]) is given by,          Time taken for distance (\[{{s}_{2}}\]) is given by,           Total distance covered = \[{{s}_{1}}+{{s}_{2}}\]         Total time taken =\[{{t}_{1}}+{{t}_{2}}\] \[\therefore \]\[Average\,velocity=\frac{total\,dis\tan ce}{total\,time\,taken}=\frac{{{s}_{1}}+{{s}_{2}}}{{{t}_{1}}+{{t}_{2}}}=\frac{{{s}_{1}}+{{s}_{2}}}{({{s}_{1}}/{{\upsilon }_{1}})+({{s}_{2}}/{{\upsilon }_{2}})}=\frac{\left( {{s}_{1}}+{{s}_{2}} \right){{\upsilon }_{1}}{{\upsilon }_{2}}}{{{s}_{1}}{{\upsilon }_{2}}+{{s}_{2}}{{\upsilon }_{1}}}\]