# Is instantaneous velocity the same as average velocity?

Instantaneous velocity can be equal to average velocity when the acceleration is zero or the velocity is constant, because all instantaneous velocities are equal to each other and likewise to the average velocity in this case. When an object is accelerating, its instantaneous velocity will not be equal to its average velocity; instead, they are both less than its average velocity.

## Can average speed and instantaneous speed be equalized?

Yes, immediate and average speeds can be the same (and can be different). The most basic situation is when a body moves at a constant pace. In this instance, its instantaneous speed is constant at all times, and its average speed throughout all time intervals is constant. For example, if a body moves at a rate of 5 meters per second for half of one minute and 10 meters per second for the other half, then its average speed is 5 meters per second, but its instantaneous speed was 0 meters per second at some points during that minute and 50 meters per second at others.

There are two ways that average and instantaneous speeds can be equal: either both are constant or both vary in direct proportion to each other. Let's look at some examples.

First, suppose that an object travels for a quarter of a mile in ten seconds, then stops and remains at rest for another quarter of a mile. Its average speed over that distance was 25 miles per hour, but its instantaneous speed was only 2 miles per hour at any point during the trip. Therefore, its average speed and its instantaneous speed were not the same - they differed by a factor of four!

Now let's say that an object travels for three quarters of a mile in twenty minutes, then stops and remains at rest for another quarter of a mile.

## What is the difference between instantaneous and average?

The absolute value of instantaneous velocity is used to calculate instantaneous speed, which is always positive. Divide the total distance traveled by the time elapsed to get the average speed. Average speed does not change regardless of whether the vehicle is moving forward or backward.

Instantaneous speed varies over time, while average speed is a constant value. The two are not equal unless the vehicle is standing still at some point in the journey. For example, if a driver travels for several miles at 50 miles per hour and then stops for several minutes before continuing on his way at 10 miles per hour, the average speed over that entire trip was 25 miles per hour but the driver experienced significant increases and decreases in speed during his journey.

Average speed reflects the overall performance of the vehicle's engine and other components such as its transmission and drivetrain. It is usually displayed on vehicles with odometers. While driving at a constant speed, divide the total distance traveled by the time it took to travel that distance to obtain the average speed. For example, if it takes you five hours to drive 250 miles at 55 miles per hour, your average speed is 40 miles per hour. If your destination is 80 miles away and you want to get there in less than an hour, your average speed was 20 miles per hour.

## How is instantaneous speed calculated?

The slope of a position-versus-time graph at a given moment represents instantaneous velocity at that point. Instantaneous speed can also be expressed as change in position divided by time between changes.

Instantaneous speed depends on both position and time. If you stop moving for some time, your speed will decrease until it reaches zero. At any given instant, only one value of speed exists; when we say "instantaneous speed," we mean the rate of change of speed with respect to position.

As an example, consider a car traveling down a hill at a constant speed of 60 miles per hour. The position function of speed is simply the number of miles driven, so speed is constantly increasing by 6 miles per hour. However, because the car is still driving down the hill, it must be accelerating in order to stay at its current position - otherwise it would reach the bottom first! The car is speeding up therefore it's instantaneous speed is greater than 6 miles per hour. If there was no limit to how fast the car could go, its speed would continue to increase indefinitely until it reached 90 miles per hour or more!

## Is the final velocity not equal to the initial velocity when the acceleration is zero?

If the average acceleration is zero across the whole distance traveled, the end velocity is equal to the starting velocity, which is (inconveniently) equal to the average velocity. This means that the final velocity will always be equal to the initial velocity.

In other words, if you want to travel a certain distance using constant velocity, you should always use a constant acceleration so that you can reach your destination at any time. This is important to know because it shows that constant velocity does not mean "steady speed" - rather, it means "speed plus constant acceleration".

For example, say you are traveling in a car with a velocity of 10 miles per hour and you apply force to the steering wheel which causes the car to turn left. The car's acceleration due to this force is positive but since it is just turning left there is no change in velocity so the final velocity will still be 10 miles per hour. If you then stop applying force to the steering wheel the car will continue moving left but now at a decreasing speed because of the average acceleration being negative. At some point the force you are applying to the steering wheel will be zero and at that moment the car will come to a complete stop.

This example shows that even though the average acceleration was zero, the final velocity was not.

## What is the zero average speed and average velocity?

The average speed cannot be 0 unless the body remains immobile during a specified time span. Average speed is defined as the ratio of a body's total distance traveled to the total time period required to cover that distance. The average velocity, on the other hand, can be zero. This occurs when the body stays in one place long enough for its position to be computed using a mean value (which is zero).

For example, if a body moves a distance of 10 meters in 5 seconds and then stops, its average velocity would be 0 m/s. However, its actual velocity could have been any number between -10 m/s and 10 m/s based on how far back it went before stopping. In this case, the average velocity was also 0 m/s but the limit of averaging only takes into account the time period during which the body was moving so there was never really a guarantee that its average velocity would end up being 0 m/s.

When computing averages, it is important to specify whether you are using the word "average" in its mathematical sense or in its popular meaning. In mathematics, the word "average" always refers to statistical average. That is, it is a way to calculate the numerical value that represents the center of gravity of a group of data points. There are two main types of averages: geometric and harmonic. Geometric averages give equal weight to all samples taken from a population.

##### Shari Torres

Shari Torres is an English teacher who loves to help her students succeed. She has been teaching for over 8 years, and she truly enjoys the challenge of each new assignment.

#### Disclaimer

BartlesVilleSchools.org is a participant in the Amazon Services LLC Associates Program, an affiliate advertising program designed to provide a means for sites to earn advertising fees by advertising and linking to Amazon.com.