# Average Velocity...1

Discussion in 'Calculus' started by nycmathguy, Mar 26, 2022.

1. ### nycmathguy

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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?

nycmathguy, Mar 26, 2022
2. ### MathLover1

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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:

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MathLover1, Mar 26, 2022
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3. ### nycmathguy

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

You say?

Average Velocity...2

nycmathguy, Mar 27, 2022
4. ### MathLover1

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yes

MathLover1, Mar 27, 2022
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