# Calculating Average Speed for a Particle Traveling at Two Different Velocities

• Indranil
In summary, the problem requires expressing the average speed of a particle, which travels half of its distance with speed v1 and the other half with speed v2, in terms of v1 and v2. By setting up the right equations and substituting the total time in the equation for average speed, the average speed can be calculated solely based on v1 and v2.
Indranil

## Homework Statement

A particle covers half of its total distance with speed v1 and the rest half distance with speed v2 . Its average speed during the complete journey is what?

## The Attempt at a Solution

As I know Vav = S / t. What is the concept behind it?

I suppose you have to express the average speed in terms of ##v_1## and ##v_2##.

stockzahn said:
I suppose you have to express the average speed in terms of ##v_1## and ##v_2##.
How to express? the question is above and I only know Vav = d / t or s / t. There is no data for D or S and t, the data is only for v1 and v1. So how to calculate?

By establish the right set of equations, the distance ##s## is canceled and you find the average speed ##\overline{v}## only depending on the velocities ##v_1## and ##v_2##. Hint: Start with the equation expressing the the total time needed ##t## with the variables ##s##, ##v_1## and ##v_2##

stockzahn said:
By establish the right set of equations, the distance ##s## is canceled and you find the average speed ##\overline{v}## only depending on the velocities ##v_1## and ##v_2##. Hint: Start with the equation expressing the the total time needed ##t## with the variables ##s##, ##v_1## and ##v_2##
Still, I don't understand your point. Could you simplify a little bit, please?

Indranil said:
How to express? the question is above and I only know Vav = d / t or s / t. There is no data for D or S and t, the data is only for v1 and v1. So how to calculate?
So, just let ##D## be unspecified, and express everything in terms of ##D##. After all, nobody told you what the values of ##v_1## and ##v_2## are, but that does not seem to bother you. Not knowing ##D## should not bother you either.

Indranil said:
Still, I don't understand your point. Could you simplify a little bit, please?

$$\overline{v}=\frac{s_{tot}}{t_{tot}}$$

If you express ##t_{tot}## as sum of the two times needed to travel the entire distance ##s_{tot}## with the different velocities (and you know that the two distances are equal), you can substitute the total time in your first equation, simplify the resulting equation and you're done.

## What is S(avg)?

S(avg) is a statistical measure that represents the average or mean deviation of a set of data points from their mean or expected value. It is also known as the standard deviation.

## Why is it important to calculate S(avg)?

Calculating S(avg) is important because it provides valuable information about the spread or variability of a data set. It helps in understanding the distribution of the data and making meaningful comparisons between different sets of data.

## How is S(avg) calculated?

S(avg) is calculated by taking the square root of the variance, which is the average of the squared deviations from the mean. The formula for S(avg) is: S(avg) = √[∑(x - x̄)^2 / (n - 1)], where x is each data point, x̄ is the mean of the data set, and n is the total number of data points.

## What are the units of S(avg)?

The units of S(avg) are the same as the units of the data set. For example, if the data set is in meters, the units of S(avg) will also be in meters.

## Can S(avg) be negative?

No, S(avg) cannot be negative. Since it is the square root of the variance, which is always a positive number, S(avg) will always be positive or zero.

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