Average Velocity...1

[nycmathguy]

Calculus 1
Section 1.4

I have not studied the derivative so far in the textbook.

Questions:

1. What is the average velocity?

2. Can you provide a graphical interpretation of the average velocity?

 

[MathLover1]

What is Average Velocity?
Average velocity is a vector quantity. Average velocity is defined as the change in position or displacement (∆x) divided by the time intervals (∆t) in which the displacement occurs. The average velocity can be positive or negative depending upon the sign of the displacement. The SI unit of average velocity is meters per second (m/s or ms^-1).0



To calculate the average velocity, we need to divide the total displacement by the total time elapsed as follows:

Where ΔV is the average velocity, Δx is the displacement, Δt is the total time, xf and x0 are the initial and final positions, tf and t0 are the starting and ending times.

If the starting time is zero, then the formula becomes:

Average velocity in a distance-time graph is shown below:

Example
During a 4 s time interval, the runner’s position changes from x1 = 60 m to x2= 40 m. What is the runner’s average velocity?

Solution:

The change in the displacement of the runner is calculated as follows:

 

[nycmathguy]

What is Average Velocity?
Average velocity is a vector quantity. Average velocity is defined as the change in position or displacement (∆x) divided by the time intervals (∆t) in which the displacement occurs. The average velocity can be positive or negative depending upon the sign of the displacement. The SI unit of average velocity is meters per second (m/s or ms^-1).0



To calculate the average velocity, we need to divide the total displacement by the total time elapsed as follows:
View attachment 2322

Where ΔV is the average velocity, Δx is the displacement, Δt is the total time, xf and x0 are the initial and final positions, tf and t0 are the starting and ending times.

If the starting time is zero, then the formula becomes:

View attachment 2323
Average velocity in a distance-time graph is shown below:

View attachment 2325
Example
During a 4 s time interval, the runner’s position changes from x1 = 60 m to x2= 40 m. What is the runner’s average velocity?

Solution:

The change in the displacement of the runner is calculated as follows:
View attachment 2326

Thank you very much. Great notes.
According to the late James Stewart, average velocity is (change in position)/(time elapsed).

You say?

Also, how about the link below?

Average Velocity...2

 

[MathLover1]

yes

 

[nycmathguy]

yes

Ok. I will do calculus 1 problems today. We will alternate between college algebra and calculus 1. However, when we get to calculus 2 and 3, I will not strictly study calculus 2 and 3.