Magnitude of average velocity and average speed

[J.live]

Homework Statement

An electron moves in the positive x-direction a distance of 2.44 m in 3.10 *10-8 s, bounces off a moving proton, and then moves in the opposite direction a distance of 1.68 m in 3.53*10-8 s.

The Attempt at a Solution

to find the average velocity I used the distance formula to find magnitude divide it by the c

Sqrt (2.44)^2+(1.68)^2 / (3.53*10^8 - 3.10*10^8) ?


for the average speed

(2.44 - 1.68) / (3.53*10^8 - 3.10*10^8)?


Can someone explain it by showing some work? I keep getting the wrong answer.

 

[cepheid]

for the average speed

(2.44 - 1.68) / (3.53*10^8 - 3.10*10^8)?


Can someone explain it by showing some work? I keep getting the wrong answer.

This part is wrong for sure. The average speed would be the total distance traveled (without regard for direction) divided by the total time elapsed. The total time elapsed would be the SUM of the two time intervals, not the difference between them, right?

 

[cepheid]

As for the first part of the question, your method for finding the net displacement is also wrong. That Pythagorean distance formula you used does not apply, because the two vectors aren't perpendicular. They are anti-parallel (meaning one is in the +x direction, and one is in the -x direction). So they lie along the same line, making this effectively a 1D problem. To add up the two vectors, all you end up having to do is subtract the two distances. Draw a picture and you'll see what I mean.

A more intuitive way to arrive at that answer is to think about what the net displacement actually means physically: it is how far from its starting point the particle ends up.

My comment about the time interval also applies here as well.

 

[J.live]

Thank you.

 

[rwisz]

The average velocity of an object is defined as the displacement divided by the time taken to cover that displacement. In this case, the electron covers a total displacement of 2.44 m + 1.68 m = 4.12 m in a total time of (3.53*10^-8 s - 3.10*10^-8 s) = 4.30*10^-9 s. Therefore, the average velocity of the electron is:

Average velocity = (4.12 m)/(4.30*10^-9 s) = 9.58*10^8 m/s

Note that the magnitude of the average velocity is the absolute value of this answer, which is 9.58*10^8 m/s.

On the other hand, the average speed of an object is defined as the total distance traveled divided by the total time taken. In this case, the electron travels a total distance of 2.44 m + 1.68 m = 4.12 m in a total time of (3.53*10^-8 s - 3.10*10^-8 s) = 4.30*10^-9 s. Therefore, the average speed of the electron is:

Average speed = (4.12 m)/(4.30*10^-9 s) = 9.58*10^8 m/s

Note that the average speed is the same as the magnitude of the average velocity in this case, since the electron is only moving in one direction. However, if the electron were to travel in different directions at different speeds, the average speed and average velocity would be different.

In summary, the average velocity and average speed of the electron in this scenario can be calculated by dividing the total displacement or total distance by the total time taken. It is important to understand the definitions and units of these quantities in order to correctly calculate them.