Question

An object is moving along the circumference of a circular track of radius R. What is average velocity of the object when it covers 3th4 of its circumference in 2 s

Answer 1

Given:

An object is moving along the circumference of a circular track of radius R.

To find:

Average velocity of the object when it covers 3/4th of its circumference in 2 sec?

Calculation:

First of all, it's important to calculate the displacement of the object:

• Displacement is the shortest length between starting and stopping point.

• Refer to DIAGRAM.

• Let displacement be 'd'.

$\rm \: d = \sqrt{ {R}^{2} + {R}^{2} }$

$\rm \implies\: d = R \sqrt{2}$

Now, let average velocity be 'v':

$\rm \: v = \dfrac{total \: displacement}{total \: time}$

$\rm \implies\: v = \dfrac{R \sqrt{2} }{2}$

$\rm \implies\: v = \dfrac{R }{ \sqrt{2} }$

So, average velocity is R/√2 m/s.

Answer 2

Given : A particle is moving along the circumference of a circular track of radius R m.  

To Find : the average velocity of particle when it covers 3/4th of its circumference in 2 second  

Solution:

a circular track of radius R  m.  

Complete circumference =  360°

(3/4) * 360° = 270°  

Hence Displacement =  √r² + r²  = r√2   = R√2  m  as radius r = R m

Time = 2

average velocity of particle  = Displacement  / Time

=> average velocity of particle  = R√2  /2   = R/√2  m/s

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