Average vs. Instantaneous Velocity: Difference & Uses

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  • 0:03 Calculating Your Velocity
  • 1:01 Average vs.…
  • 2:22 Graphic Representations
  • 3:31 When Are the…
  • 4:02 When To Use Each Velocity
  • 4:50 Lesson Summary
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Lesson Transcript
Betsy Chesnutt

Betsy teaches college physics, biology, and engineering and has a Ph.D. in Biomedical Engineering

Expert Contributor
Matthew Bergstresser

Matthew has a Master of Arts degree in Physics Education. He has taught high school chemistry and physics for 14 years.

What is the difference between average and instantaneous velocity? How do you calculate each of these and when do you use them? This lesson will help you understand these common terms and know when to use each one.

Calculating Your Velocity

Jack was on his way to school when he had to stop his car to let a train pass. At that point, he had already driven three miles from his house, and he still had five more miles to go to reach his school. As he sat in his car waiting, Jack tried to calculate how fast he would need to drive to still make it to school on time.

He knew that he needed to calculate his velocity, but he wasn't really sure how to do that. He remembered from his physics class that velocity was defined as the rate of change of an object's position.

However, to calculate his velocity, he didn't know if he should use the total distance he was traveling to school (eight miles), the distance he had already driven (three miles), or the distance he still had to go (five miles). Also, what about the fact that he was now stopped waiting on the train? Wasn't his current velocity zero since his car wasn't moving?

Wow! Determining the velocity of an object isn't as simple as Jack thought at first. What can he do?

Average vs. Instantaneous Velocity

The issue Jack is facing is that there are two different ways that velocity can be calculated, and they each give you very different information about an object's motion. The average velocity of an object is found by dividing its total displacement by the total time it took to move from one place to another.

average velocity = change in position / change in time = d / t

Average velocity doesn't tell you exactly how fast an object is moving at every instant in time. The object can speed up, slow down, and even stop for a while, and this will not directly affect its average velocity. If it took Jack a total of 30 minutes to travel the eight miles from his house to school, what was his average velocity?

Vav = d / t = (8 miles ) / (30 minutes) = 0.27 miles/min

In contrast, instantaneous velocity is the velocity of the object at a single instant in time. This may or may not be the same as the average velocity over a longer time interval. In Jack's case, while he is sitting still waiting for the train to pass, his instantaneous velocity is zero because his car is not currently moving at all. However, his average velocity on the entire trip to school will not be zero even though the instantaneous velocity was zero for a small part of the trip.

Graphic Representations

If you represent the position of an object over time on a graph, you can use the graph to find both the average and instantaneous velocity of the object at any time. Let's look at a position versus time graph of Jack's entire trip to school to see how this works:

Position vs. time graph
Position vs. time graph

In the first six minutes, Jack went three miles. Then, he stopped and waited on the train for nine more minutes, and finally, he traveled the remaining five miles to school in fifteen minutes.

We can find Jack's average velocity from the graph by drawing a line between the beginning point and the ending point and then finding the slope of that line.

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Additional Activities

Velocities of a Space Shuttle During Launch

When working with the motion of objects (kinematics), we have different types of velocities. There is speed, which is how fast an object is moving (the direction of an object's motion is irrelevant when reporting an object's speed). Next is instantaneous velocity, which is the velocity of an object at a specific instant in time (includes the direction of the object's motion). Average velocity is the displacement of the object (straight line distance from an object's starting point to its current location) divided by the time it took to get from these two locations.

When a rocket is launched, it undergoes a varying acceleration, which means its acceleration is not constant, thereby making its velocity not constant. Let's make some comparisons of instantaneous velocities and average velocities for the first 12 seconds of a space shuttle launch.

Space Shuttle Rocket Velocities Activity

Below is a table with data for a space shuttle launch. All of our distances will be in miles, so we'll need to convert the altitude into miles using the conversion factor, 1 mile = 5,280 feet. Divide each value in feet by 5,280 to get the value in miles.

Time Altitude (feet) Velocity (miles/hour)

Displacement is the initial position minus the final position, or {eq}s_f-s_i {/eq}.

The average velocity is displacement divided by time, or {eq}v_{avg}=\dfrac{s_f-s_i}{t_f-t_i} {/eq}.

Fill out the table below using the data provided in the previous table.

Time (s)Time (hr) Altitude (feet) Altitude (miles)Velocity (miles/hour)Instantaneous velocity (miles/hour)

Calculate the average velocity between:

a) 0 - 4 seconds

b) 0 - 6 seconds

c) 0 - 8 seconds

d) 0 - 10 seconds

e) 0 - 12 seconds

Compare the instantaneous velocities at 4, 6, 8, 10 and 12 seconds to the average velocities you just calculated. Which velocity has the higher value?

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