Question

a person moving on a circular track one round in three parts of equal lenght with constant speed of v ,2v,3v respectively . the average speed of object for the entire trip is

Answer 1

Let the Radius of the Circular Path be r.

∴ Perimeter of the Circular path or the Total distance traveled by it (S) = 2πr

∴ If the Person is covering the distance is equal three intervals, then distance covered in each interval = 2πr/3

At First,

Speed = v

∴ Time taken = (2πr/3)/v

⇒ T₁ = 2πr/3v

Similarly, T₂ = 2πr/6v and T₃ = 2πr/9v

∴ Total time = 2πr/3v + πr/3v + 2πr/9v

⇒ T = (6πr + 3πr + 2πr)/9v

∴ T = 11πr/9v

Average Speed = Total distance/Total time.

⇒ Average Speed = 2πr/(11πr/9v )

∴ Average Speed = 18v/11

Hope it helps.  

Answer 2

HEY DEAR ... ✌️

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Here's , Your Answer :-

=) 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 .

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HOPE , IT HELPS ... ✌️