Question

A particle is moving along the circumference of a circular track of radius 2 m. What is the average velocity of particle when it covers 3/4th of its circumference in 4√2 second?
explain it​

Answer 1

Given : A particle is moving along the circumference of a circular track of radius 2 m.  

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

Solution:

a circular track of radius 2 m.  

Complete circumference =  360°

(3/4) * 360° = 270°  

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

Time = 4√2

average velocity of particle  = Displacement  / Time

=> average velocity of particle  = 2√2  /4√2   = 1/2  m/s

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Answer 2

Given:

A particle is moving along the circumference of a circular track of radius 2 m.

To find:

Average Velocity when the body covers 3/4th of its circumference in 4√2 second?

Calculation:

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

• So, after ¾th of journey, the displacement can be found using Pythagoras' theorem.

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

Now, average velocity can be calculated from ratio of displacement and time:

$\rm \: avg. \: v = \dfrac{displacement}{time}$

$\rm \implies \: avg. \: v = \dfrac{2 \sqrt{2} }{4 \sqrt{2} }$

$\rm \implies \: avg. \: v = 0.5 \: m {s}^{ - 1}$

So, average velocity is 0.5 m/s.