a person moving on a circular track completes one round in three parts of equal length with constant speed of v, 2v, 3v respectively. The average speed of object for the entire trip is
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Let the person be moving on a circular track of radius "r"
therefore the circumference of circle is 2πr
if the lesson completes rounds in three dual parts then the length of each part will be
2πr/3
and the velocity for each part is given to be as v, 2v, 3v respectively...
Average speed =Total distance / Total time
=2πr/(2πr/(3v) +2πr/(3*2v)+2πr/(3*3v))
=2π/(2π/(3v) +2π/(6v) +2π/(9v))
=1/(1/v*(1/3+1/6+1/9)
=1/(1/v*((6+3+2)/18)
=1/(1/v*(11/18))
=18v/11 is the average speed...
hope this helps!! ^_^
therefore the circumference of circle is 2πr
if the lesson completes rounds in three dual parts then the length of each part will be
2πr/3
and the velocity for each part is given to be as v, 2v, 3v respectively...
Average speed =Total distance / Total time
=2πr/(2πr/(3v) +2πr/(3*2v)+2πr/(3*3v))
=2π/(2π/(3v) +2π/(6v) +2π/(9v))
=1/(1/v*(1/3+1/6+1/9)
=1/(1/v*((6+3+2)/18)
=1/(1/v*(11/18))
=18v/11 is the average speed...
hope this helps!! ^_^
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