Question

A man starts walking from point a ina circular path of π7 m and compete round in 10 sec what is his speed and velocity

Answer 1

$\rule{300}{2}$

GIVEN :-

$\textsf{Length of the circular path = }\sf{\ \pi 7 m}$

$\textsf{Time taken to complete the round(travel a distance }\sf{of\ \pi 7\ m) = 10\ s}}$

TO FIND :-

$\textsf{The speed and the velocity of the man.}$

FORMULAS TO BE USED :-

$\bigstar\ \displaystyle{\sf{Speed=\frac{Total\ distance }{Total\ time} }}$

$\bigstar\ \displaystyle{\sf{Velocity=\frac{Total\ displacement }{Total\ time} }}$

SOLUTION :-

$\textsf{According to question, distance = }\sf{\pi 7\ m}\\\\\sf{Time\ taken = 10\ s}$

$\displaystyle{\sf{Speed=\frac{Total\ distance }{Total\ time} }}\\\\ \displaystyle{\sf{\implies Speed=\frac{\pi 7}{10} }}$

$\underline{\sf{If\ we\ put\ \pi =\frac{22}{7},\ then, }}$

$\displaystyle{\sf{\implies Speed=22\times\frac{1}{10} }}\\\\\boxed{ \displaystyle{\sf{\implies Speed=\frac{11}{5}\ m/s }}}$

$\textsf{As the path is circular, so after 1 round, the man returns to his }\\\textsf{initial position. So, displacement = 0.}$

$\displaystyle{\sf{Velocity=\frac{Total\ displacement }{Total\ time} }}$

$\displaystyle{\sf{\implies Velocity=\frac{0 }{10} }}\\\\\boxed{\displaystyle{\sf{\implies Velocity=0\ m/s }}}$

$\rule{300}{2}$

Answer 2

Given :-

Distance of circular path is π7 m

And time to cover this distance is 10 seconds

To find

we have to find the Speed and velocity of man in circular path

So ,By formula

$\bigstar{\boxed{\sf{Speed=\dfrac{ Distance }{Time }}}}$

Put the given values in the formula to find the Speed !

$\longmapsto\sf Speed = \dfrac{\pi 7}{10}\\ \\ \sf\ \ \ \ Value \ of \ \pi =\dfrac{22}{7} \\ \\ \longmapsto\sf Speed =\dfrac{ \dfrac{22}{\cancel{7}}\times \cancel{7}}{10}\\ \\ \longmapsto\sf Speed = \cancel{\dfrac{22}{10}}\\ \\ \longmapsto\sf Speed = \dfrac{11}{5}m/s$

$\underline{\sf{\dag\ \ Speed \ of \ man = \dfrac{11}{5} m / s}}$

• Now the velocity of man ,

Displacement :- Shortest distance between initial and final position of a body

In a circular path man returns to his initial velocity

So , Initial velocity = final velocity, it's displacement becomes Zero

$\bigstar{\boxed{\sf{Velocity=\dfrac{Displacement}{Time }}}}$

• We have ,

• Displacement = 0

• Time = 10 seconds

• Velocity = ?

$\longmapsto\sf Velocity =\cancel{\dfrac{0}{10}}\\ \\ \longmapsto\sf Velocity= 0m/s$

$\underline{\textsf{\textbf{\dag\ \ \ velocity= 0m/s}}}$

$\boxed{\sf{\dag \ \ speed\ of \ man = \dfrac{11}{5}m/s }}$

$\boxed{\sf{\dag \ \ velocity \ of \ man = 0 m/s }}$