Question

a partical covers one fourth of its distance with speed v and reamining three fourth with 2v . the average speed of partical is ​

Answer 1

Correct question:-

A particle covers one fourth of its distance with speed v and remaining three fourth with 2v.The average speed of the particle is.

Given:-

→Speed of the particle with which it covers one-fourth of the distance=v

→Speed of the particle with which it covers remaining three-fourth of the distance=2v

To find:-

→Average speed of the particle

Solution:-

Let the total distance be d.

Thus,distance in the 2cases will be:-

$= > d1 = \frac{d}{4}$

$= > d2 = \frac{3d}{4}$

We know that:-

Time=Distance/Speed

=>t1=d1/v

=>t2=d2/2v

$= > t1 = \frac{d}{ \frac{4}{v} }$

$= > t2 = \frac{3d}{ \frac{4}{2v} }$

Now,the formula for finding average speed is:-

=>Vav=Total distance/Total Time

=>Vav= d1+d2/t1+t2

$= > \frac{d}{ \frac{d}{ \frac{4}{v} } + \frac{3d}{ \frac{4}{2v} } }$

$= > \frac{d}{ \frac{d}{4v} + \frac{3d}{8v} }$

$= > \frac{d}{ \frac{5d}{8v} }$

$= > d \times \frac{8v}{5d}$

$= > \frac{8v}{5}$

Thus,average speed of the particle is 8v/5.