Question

a particle covers one fourth of its distance with speed v and remaining three fourth with speed 2v. the average speed of particle is:1.8/5v,2.3/2v,3.4/3v,4.7/5v

Answer 1

Answer: 1.
`(8v)/(5)`

Explanation: Speed is a variable in Physics defined by the rate at which an object go through a distance. It can be calculated as:

`speed=(distance)/(time)`

A fourth of distance with speed v takes:

`speed=(distance)/(time)`

`time=(distance)/(speed)`

`time=(1)/(4v)`

The rest of the distance with speed 2v takes:

`time=(3)/(4*2v)`

`time=(3)/(8v)`

Average speed is given by:

`average=(distance_(traveled))/(time_(travel))`

Total time to cover the distance:

`time=(1)/(4v)+(3)/(8v)`

`time=(2+3)/(8v)`

`time=(5)/(8v)`

Total distance traveled:

`d=(1)/(4) +(3)/(4)`

d = 1

average = 1 ÷
`(5)/(8v)`

`average=(8v)/(5)`

The average speed of particle is 8/5v.

Answer 2

`Speed = (8v)/(5)`

Step-by-step explanation:

Given

`Speeds: v\ and\ 2v`

Required

Determine the average speed

First, we need to determine the time spent on the journey

`Time = Distance/Speed`

For the first
`(1)/(4)th`

`T_1 = (1)/(4)/v`

`T_1 =(1)/(4v)`

For the next
`(3)/(4)th`

`T_2 = (3)/(4)/2v`

`T_2 = (3)/(8v)`

`Total\ Time = T_1 +T_2`

`T = (1)/(4v) + (3)/(8v)`

`T = (2+3)/(8v)`

`T = (5)/(8v)`

Average Speed is then calculated as thus:

`Speed = Distance/Time`

`Speed = ((1)/(4) + (3)/(4))/(5)/(8v)`

`Speed = ((1+3)/(4))/(5)/(8v)`

`Speed = ((4)/(4))/(5)/(8v)`

`Speed = 1/(5)/(8v)`

`Speed = 1 * (8v)/(5)`

`Speed = (8v)/(5)`

Hence;

Option 1 answers the question