# How to calculate S(avg)?

## 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?

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

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?

stockzahn
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 $v_2$

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?

Ray Vickson
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.

stockzahn
Homework Helper
Gold Member
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.