# Is acceleration correlated with an instantaneous velocity?

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

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!!

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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?

Mark44
Mentor
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.
You pull your foot off the gas when you see the cop, then at that instance, velocity also decreases?
Yes, of course.
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.

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

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.

HallsofIvy
Homework Helper
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.

Redbelly98
Staff Emeritus
Homework Helper
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

HallsofIvy
Homework Helper
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.