Physics Lesson 3.5.4 - Average and Instantaneous Velocity

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Welcome to our Physics lesson on Average and Instantaneous Velocity, this is the fourth lesson of our suite of physics lessons covering the topic of Speed and Velocity in 1 Dimension, you can find links to the other lessons within this tutorial and access additional physics learning resources below this lesson.

Average and Instantaneous Velocity

The approach is the same as for Average and Instantaneous Speed. Thus, Average Velocity < v > represents the total Displacement divided by the total Time taken. The concept of average velocity is particularly useful when dealing with non-uniform motion.

Mathematically, we have:

< v > = ∆xtot/ttot

As for Instantaneous Velocity v, again we take two neighbouring values for Position and Time. In this way, we obtain one interval for each quantity, namely ∆x and ∆t. Therefore, we obtain the equation

v = ∆x/∆t


Calculate the average velocity of the entire motion and the instantaneous velocity at t = 4.0 s for a moving object whose Position vs Time graph is shown in the figure below.

Physics Tutorials: This image shows


From the graph, we see that the initial position is xi = 9.0m and the final position is xf = 2.0m, the initial time is ti = 0 and the final time is tf = 6.5s. Therefore, applying the formula of average velocity

< v > = ∆xtot/ttot = xf - xi/tf - ti

we obtain after the substitutions

< v > = 9.0m - 2.0m/6.5s - 0s
= 7.0m/6.5s
= 1.1 m/s

(The result is written at one decimal place to fit the clues. Look at the tutorail Significant Figures and Their Importance).

As for the instantaneous velocity at the instant required (at t = 4.0s), again we take two surrounding values for each quantity shown in the graph (two for position and two for the time). These values must be as close as possible to the point required. For example, we can choose t1 = 3.8s and t2 = 4.2s. From the graph, we can see that the corresponding values of position are x1 = 6.2m and x2 = 6.8m as shown below.

Physics Tutorials: This image shows

Using the equation of the instantaneous velocity

v = ∆x/∆t

we obtain after substituting the known values:

v = x2-x1/t2-t1
6.8m - 6.2m/4.2s - 3.8s
= 0.6m/0.4s
= 1.5 m/s

Remark! From Mathematics, it is known that the slope of a graph (otherwise known as gradient) at a certain point is obtained by dividing the change in vertical coordinate to the change in the horizontal one for a small interval surrounding the given point. This can be observed in our example as well. Look at the magnified section of the graph around the instant t = 4.0 s.

Physics Tutorials: This image shows

Therefore, we obtain a very important rule in Kinematics:

"The slope (gradient) of the Position vs Time graph gives the Velocity."

This rule helps a lot in understanding the properties of velocity and gives it a mathematical meaning.

You have reach the end of Physics lesson 3.5.4 Average and Instantaneous Velocity. There are 4 lessons in this physics tutorial covering Speed and Velocity in 1 Dimension, you can access all the lessons from this tutorial below.

More Speed and Velocity in 1 Dimension Lessons and Learning Resources

Kinematics Learning Material
Tutorial IDPhysics Tutorial TitleTutorialVideo
3.5Speed and Velocity in 1 Dimension
Lesson IDPhysics Lesson TitleLessonVideo
3.5.1What is Speed? How do we measure it?
3.5.2The meaning of Average and Instantaneous Speed
3.5.3What is Velocity? How do we measure it?
3.5.4Average and Instantaneous Velocity

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