Calculating Average Speed for a Particle Traveling at Two Different Velocities

[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?

Homework Equations

The Attempt at a Solution

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

 

[stockzahn]

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?

 

[stockzahn]

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 $v_2$

 

[Indranil]

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?

 

[Ray Vickson]

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]

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.