Average Speed Vs. Direct Average?

[Simon777]

I'm having trouble differentiating between the definition of average in physics and a traditional average.

For example, say a car travels 100km for 2 hours then travels 80km for 1 hour. The average speed for the first portion is 50km/hr and the average speed for the second portion is 80km/hr.

Here is where I have an issue. The average speed for the entire trip is 60km/hr(total distance over total time), but taking a traditional direct average where you add everything and divide by the sum of how many things you added together, I get 65km/hr. Why are these different? If anyone can define these two types of averages for me, I'd greatly appreciate it.

 

[bp_psy]

I'm having trouble differentiating between the definition of average in physics and a traditional average.

For example, say a car travels 100km for 2 hours then travels 80km for 1 hour. The average speed for the first portion is 50km/hr and the average speed for the second portion is 80km/hr.

Here is where I have an issue. The average speed for the entire trip is 60km/hr(total distance over total time), but taking a traditional direct average where you add everything and divide by the sum of how many things you added together, I get 65km/hr. Why are these different? If anyone can define these two types of averages for me, I'd greatly appreciate it.

We define average speed as v= Total distance /time.It is a physical definition that can be a useful in some situations.We can also define Vav as the average of a set of speeds. This is a statistical definition and can be useful is some situation.For example If we want to find the average velocity of a bullet coming out of a gun we make multiple measurements of that velocity and average it.They are totally different concepts.

 

[robphy]

In physics, "Average velocity" is a time-weighted average of velocity.

https://www.physicsforums.com/showthread.php?p=322150#post322150

(I feel this point needs to be emphasized first... before the "displacement/time" definition.)

 

[Simon777]

Thank you both, these two concepts make sense to me now. To further solidify this in my mind, could either of you state a situation where the physical definition of average speed is useful?

I like the example for the statistical definition of an average with finding an average velocity of a bullet and will remember that, but now I need an example for the physical definition to help visualize these concepts.

 

[robphy]

Suppose you had to make the trip where you
"travels 100km for 2 hours then travels 80km for 1 hour".
(You worked out the velocities on each leg.)

Could you make the same trip (with same starting and ending positions in the same total time)
with a constant velocity? If so, what is that velocity?

It might help if you draw a position-vs-time graph.

 

[Simon777]

Suppose you had to make the trip where you
"travels 100km for 2 hours then travels 80km for 1 hour".
(You worked out the velocities on each leg.)

Could you make the same trip (with same starting and ending positions in the same total time)
with a constant velocity? If so, what is that velocity?

It might help if you draw a position-vs-time graph.

That's a really good one, thank you. This is my first physics class in college and so far the book has done a good job of explaining the fundamentals, but I agree with you that physics books need to clearly state if there is a different definition for something like average since newcomers like me are used to the traditional definition. Regardless, I'm still enjoying the subject and will keep at it. Thank you for helping me.