Avg. Velocity = Distance Traveled / Time Traveled

[incognito301]

Do you know if these two formulas are the same?

Avg. Velocity = Distance Traveled / Time Traveled

&

Avg. Velocity = V1 + V2 / 2 (V1 = d1/t1 & V2 = d2/t2)

I have a problem that says that a plain goes from a place to another(1) and from there it goes to another place (2).

So:

t1 = 3 h & d1 = 375 km
t2 = 2 h & d2 = 250 km

and using both of the formulas I get the same Average Velocity.
So:

Formula 1 = (375/3 + 250/2)/2 = 125 m/s
.......... ----> Formula 1 = Formula 2
Formula 2 = (375 + 250)/(3+2) = 125 m/s
So I'm guessing they are the same. But my science teacher says they're not.

Do you agree with my teacher? How come?

If you think its right, can you show me a mathematical way to prove it?

Thanks.

P.S. Please answer ASAP.

 

[Doc Al]

You are only getting away with Formula 1 because the velocity is constant in your example. What if it wasn't constant?

Say the plane moved a distance of 300 km in 2 hours, then an additional 300 km in 1 hour. Compare your formulas in this case.

 

[ogb p]

I would agree with your teacher that these two formulas are not exactly the same. While they may result in the same average velocity in this specific scenario, they represent different concepts and should not be used interchangeably.

The first formula, Avg. Velocity = Distance Traveled / Time Traveled, is a basic definition of average velocity, where distance and time are directly related to each other. This formula is used when an object travels at a constant velocity over a certain distance and time period.

The second formula, Avg. Velocity = V1 + V2 / 2, is an approximation of average velocity. This formula is used when an object travels at different velocities over a certain distance and time period. It takes into account the different velocities by averaging them.

In your example, the plane travels at a constant velocity for the first leg of the journey (375 km in 3 hours) and then at a different constant velocity for the second leg (250 km in 2 hours). In this case, the two formulas will give the same result because the velocities are constant. However, if the plane were to travel at varying velocities throughout the journey, the two formulas would give different results.

To prove that these two formulas are not the same, we can use a simple counterexample. Let's say the plane traveled 500 km in 5 hours for the first leg and then 100 km in 1 hour for the second leg. Using the first formula, we get an average velocity of 100 km/h. Using the second formula, we get an average velocity of 112.5 km/h. This shows that the two formulas are not equivalent and cannot be used interchangeably.

In conclusion, while the two formulas may give the same result in certain scenarios, they represent different concepts and should not be considered the same. As a scientist, it is important to understand the concepts behind the formulas and use them appropriately in different situations.