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:

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

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 $\frac{1}{4}th$

$T_1 = \frac{1}{4}/v$

$T_1 =\frac{1}{4v}$

For the next $\frac{3}{4}th$

$T_2 = \frac{3}{4}/2v$

$T_2 = \frac{3}{8v}$

$Total\ Time = T_1 +T_2$

$T = \frac{1}{4v} + \frac{3}{8v}$

$T = \frac{2+3}{8v}$

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

Average Speed is then calculated as thus:

$Speed = Distance/Time$

$Speed = (\frac{1}{4} + \frac{3}{4})/\frac{5}{8v}$

$Speed = (\frac{1+3}{4})/\frac{5}{8v}$

$Speed = (\frac{4}{4})/\frac{5}{8v}$

$Speed = 1/\frac{5}{8v}$

$Speed = 1 * \frac{8v}{5}$

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

Hence;

Option 1 answers the question

Answer 2

Answer: 1. $\frac{8v}{5}$

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

$speed=\frac{distance}{time}$

A fourth of distance with speed v takes:

$speed=\frac{distance}{time}$

$time=\frac{distance}{speed}$

$time=\frac{1}{4v}$

The rest of the distance with speed 2v takes:

$time=\frac{3}{4*2v}$

$time=\frac{3}{8v}$

Average speed is given by:

$average=\frac{distance_{traveled}}{time_{travel}}$

Total time to cover the distance:

$time=\frac{1}{4v}+\frac{3}{8v}$

$time=\frac{2+3}{8v}$

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

Total distance traveled:

$d=\frac{1}{4} +\frac{3}{4}$

d = 1

average = 1 ÷ $\frac{5}{8v}$

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

The average speed of particle is 8/5v.