Average velocity problem~From Jay Orear book.

[Biggy_G]

Homework Statement

Car passes distance x₁ with velocity v₁
further it passes distance x₂ with velocity v₂. Find average velocity (averaged by distance), at that consider x₁ and x₂ as weighting factors.

Homework Equations

V_average=(v₁t₁+v₂t₂)/(t₁+t₂)

The Attempt at a Solution

I used substitution t=x/v and replaced t's in the formula and tried to simplify, but couldn't get correct answer.

I will be grateful for anyone's help.
Thanks

 

[Abhishekdas]

Find average velocity (averaged by distance), at that consider x₁ and x₂ as weighting factors.

What do you mean by weighting factors?

Other than that averge vel=(v1*t1+v2*t2)/t1+t2 doesn't seem wrong from any angle...

 

[gneill]

Homework Statement

Car passes distance x₁ with velocity v₁
further it passes distance x₂ with velocity v₂. Find average velocity (averaged by distance), at that consider x₁ and x₂ as weighting factors.

Homework Equations

V_average=(v₁t₁+v₂t₂)/(t₁+t₂)

The Attempt at a Solution

I used substitution t=x/v and replaced t's in the formula and tried to simplify, but couldn't get correct answer.

I will be grateful for anyone's help.
Thanks

If they want the velocity averaged by distance, then the distances become the weighting factors (so that more "weight" is given to longer distance stretches in the figuring of an average). Multiply each velocity by its "weighting factor" (which is the distance that it traveled at that speed), sum them up, and divide by the sum of the weights.

 

[Abhishekdas]

Frankly Gneill i did not exactly get you...
I have done some physics but have never come across this term "weighing factors" and i always thought that average velocity is always total displacement by total time...
Ok i will search this term up in google and then i will try and get back to you...

 

[Biggy_G]

Thanks gentlemen for replies,
The thing is I found this problem in Jay Orear's book. Chapter 2 exercise 5. I am reading the book in Russian and I think that I translated Weighting Factor correctly. When they say Average velocity, mostly authors mean Velocity averaged by time. However, as they say, weighted by distance average velocity is used in Hydrodynamics.

 

[Biggy_G]

If they want the velocity averaged by distance, then the distances become the weighting factors (so that more "weight" is given to longer distance stretches in the figuring of an average). Multiply each velocity by its "weighting factor" (which is the distance that it traveled at that speed), sum them up, and divide by the sum of the weights.

Exactly Correct answer :) Thanks