Finding Average Velocity of Entire Trip

• Bashyboy
In summary, this problem is asking for a way to find the average speed of two vectors, where one vector is travelling in a given direction and the other vector is travelling at a different direction, but the time it takes to travel the distance is different for each vector.
Bashyboy
I have been solving these sort of problems, and they follow this basic paradigm: first, they will tell me I traveled a distance D at a velocity of A, then they traveled the same distance D at a velocity of B. Why can't I simply just simply perform the following computation: (A+B)/2. I have been searching the internet for some unequivocal explanation to this sort of problem, but have found no such explanations that suffice in aiding my comprehension in solving these kinds of problem. So, it would be much appreciated if someone would could give me a good explanation of this.

Edit: I forgot to mention that the velocity A does not equal the velocity B

Last edited:
Average speed is computed as traveled distance divided into elapse time.
No doubt in your example the total distance is 2D. However the elapsed time is (D/A+D/B).
The first term is the time employed to travel distance D at speed A and the second is the same for B.
Now, if you compute the average speed, won't find (A+B)/2

Oh, so the reason why I cannot simply just add the two velocities, and divide by two, is because the time it takes to travel distance D is different with each velocity, meaning the elasped time is different than when I just add them and divide by two?

You're right.

FWIW, velocity is a vector quantity, so this particular question will also be dependent on the geometric relationship between the start and finishing points.

Whereas the above may be interpreted to be discussing speed rather than velocity.

cmb, I actually just sort of made this problem on the spot. I posed the question with the pretense that each velocity were in the same direction, but I certainly see what you are saying.

What does average velocity of an entire trip represent?

The average velocity of an entire trip represents the average speed and direction at which an object travels throughout its entire journey.

How is average velocity of an entire trip calculated?

The average velocity of an entire trip is calculated by dividing the total distance traveled by the total time taken. This gives the average speed at which the object traveled.

What are the units for average velocity of an entire trip?

The units for average velocity of an entire trip are distance over time, typically represented as meters per second (m/s) or kilometers per hour (km/h).

Can average velocity of an entire trip be negative?

Yes, average velocity of an entire trip can be negative. A negative velocity indicates that the object traveled in the opposite direction from its starting point.

What is the difference between average velocity and average speed?

Average velocity takes into account the direction of motion, while average speed only considers the magnitude of the velocity. Average velocity is a vector quantity, while average speed is a scalar quantity.

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