# Is acceleration correlated with an instantaneous velocity?

• gomer36
In summary, velocity and instantaneous velocity are considered synonymous terms, while average velocity is the change in position divided by the change in time. Acceleration and instantaneous acceleration are also considered synonymous. There is no correlation between acceleration and velocity, as they can have varying values and directions. Instantaneous velocity and acceleration can both be positive or negative, depending on the initial conditions and the direction of motion.
gomer36
Is acceleration correlated with an instantaneous velocity?

Velocity = Instantaneous Velocity
Acceleration = Instantaneous Acceleration

Change in displacement/time elapsed = Δs/Δt
Change in velocity/time elapsed = Δv/Δt

thanks

gomer36 said:
Is acceleration correlated with an instantaneous velocity?

Velocity = Instantaneous Velocity

Average velocity is not instantaneous velocity. You're in your car driving down the freeway. You're going 80 miles per hour. That's your instantaneous velocity. You see a cop so you slow to 50 for a while. The cop turns off the freeway so you pick it back up to 80 again. (This is only a hypothetical example, don't try this at home!)

Your AVERAGE velocity during your trip was, say 65 miles per hour. But you only had an instantaneous velocity of 65 for a couple of moments, once as you slowed from 80 to 50 and again as you sped up from 50 to 80.

The fact that if you went from 50 to 80 that your instantaneous velocity must have been 65 at some instant is the mean value theorem.

Clarifying your terms might help whoever's having this argument. Instantaneous velocity in an instant is not the same as average velocity over a period of time.

And, uh, always obey the law. For example, I always obey the law of gravity. You should too!

Last edited:
SteveL27 said:
Average velocity is not instantaneous velocity. You're in your car driving down the freeway. You're going 80 miles per hour. That's your instantaneous velocity. You see a cop so you slow to 50 for a while. The cop turns off the freeway so you pick it back up to 80 again. (This is only a hypothetical example, don't try this at home!)

Your AVERAGE velocity during your trip was, say 65 miles per hour. But you only had an instantaneous velocity of 65 for a couple of moments, once as you slowed from 80 to 50 and again as you sped up from 50 to 80.

The fact that if you went from 50 to 80 that your instantaneous velocity must have been 65 at some instant is the mean value theorem.

Clarifying your terms might help whoever's having this argument. Instantaneous velocity in an instant is not the same as average velocity over a period of time.

And, uh, always obey the law. For example, I always obey the law of gravity. You should too!
Thanks, appreciate this but I just want to clarify. Then there is a correlation if the velocity is instantaneous but it's not correlated if it's average? You pull your foot off the gas when you see the cop, then at that instance, velocity also decreases? And after leaving after getting a ticket, when you hit the accelerator, instantaneous velocity is also positive?

gomer36 said:
Thanks, appreciate this but I just want to clarify. Then there is a correlation if the velocity is instantaneous but it's not correlated if it's average?
Correlated with what?

Velocity and instantaneous velocity are usually considered synonyms. Average velocity is something different, being the change in position divided by the change in time. Likewise, acceleration and instantaneous accleration are considered to mean the same thing.
gomer36 said:
You pull your foot off the gas when you see the cop, then at that instance, velocity also decreases?
Yes, of course.
gomer36 said:
And after leaving after getting a ticket, when you hit the accelerator, instantaneous velocity is also positive?
The only way your velocity could be negative is if you started going backwards.

I think you might be confusing acceleration and velocity.

If you're in your car and it is parked, v = 0 and a = 0. When you drive away, your acceleration is positive until you reach some cruising speed, say 35 mph. At that point your acceleration becomes 0.

If you hit the brakes to slow down, your velocity stays positive until you stop, and your acceleration is negative.

Perhaps it would help if you explained what you mean by "correlated".

HallsofIvy said:
Perhaps it would help if you explained what you mean by "correlated".

an example if something starts to accelerate that both acceleration and instantaneous velocity are both positive.

Well, that, certainly, is NOT necessarily true. If the initial velocity is negative, say the object is going backwards, then a positive acceleration does not immediately give a positive velocity. It results in a "less negative" velocity- the object is still going backwards but more slowly.

gomer36 said:
an example if something starts to accelerate that both acceleration and instantaneous velocity are both positive.
No, acceleration and instantaneous velocity are not correlated. It is possible to have any of the following:
• positive acceleration and negative velocity
• positive acceleration and positive velocity
• negative acceleration and negative velocity
• negative acceleration and positive velocity

Thanks, Redbelly98.

• [*]positive acceleration and negative velocity
The object is moving to the left and its speed is decreasing.
[*]positive acceleration and positive velocity
The object is moving to the right and its speed is increasing.
[*]negative acceleration and negative velocity
The object is moving to the left and its speed is increasing.
[*]negative acceleration and positive velocity
The object is moving to the right and its speed is increasing.

## 1. How do you define acceleration and instantaneous velocity?

Acceleration is the rate of change of velocity with respect to time. It is a vector quantity, meaning it has both magnitude and direction. Instantaneous velocity, on the other hand, is the velocity of an object at a specific moment in time. It is also a vector quantity.

## 2. Is there a difference between average acceleration and instantaneous acceleration?

Yes, there is a difference between the two. Average acceleration is calculated by dividing the change in velocity by the change in time over a given interval. It represents the overall change in velocity during that interval. Instantaneous acceleration, on the other hand, is the acceleration of an object at a specific moment in time, and can be found by taking the derivative of the object's velocity-time graph.

## 3. How is acceleration related to velocity?

Acceleration and velocity are directly related, meaning they both affect each other. If an object's acceleration increases, its velocity will also increase. This can be seen in equations such as v = u + at, where v represents final velocity, u represents initial velocity, a represents acceleration, and t represents time.

## 4. Can acceleration and instantaneous velocity have different directions?

Yes, they can have different directions. Acceleration is a vector quantity, so it has both magnitude and direction. Instantaneous velocity also has direction, as it is a vector quantity. Therefore, it is possible for an object to have an acceleration and instantaneous velocity with different directions.

## 5. Is there a direct correlation between acceleration and instantaneous velocity?

There is a correlation between acceleration and instantaneous velocity, but it is not always direct. This means that an increase in acceleration does not always result in an equal increase in instantaneous velocity. The relationship between the two depends on factors such as the object's initial velocity, the direction of acceleration, and the duration of the acceleration.

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