# How to calculate S(avg)?

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?

## Answers and Replies

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

Indranil
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?

Homework Helper
Gold Member
By establish the right set of equations, the distance ##s## is cancelled 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##

Indranil
By establish the right set of equations, the distance ##s## is cancelled 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?

Homework Helper
Dearly Missed
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.

Homework Helper
Gold Member
Still, I don't understand your point. Could you simplify a little bit, please?

You've already presented one equation:

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

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.