# Difference between instantaneous velocity and acceleration

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Hi,

I'm just beginning to learn physics on my own. It seems that instantaneous velocity and acceleration are the same thing. Is it reasonable for me to be confused about the two? If acceleration = final velocity - initial velocity / change in time ... then how this any different from instantaneous velocity? I know that there units are different, but the equation and overall concept seems the same to me.

- Olivia

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PeroK
Homework Helper
Gold Member
I'm not sure where you have got that idea from. Acceleration is rate of change of velocity.

Okay. Then what is instantaneous velocity?

PeroK
Homework Helper
Gold Member
Okay. Then what is instantaneous velocity?
Instantaneous velocity is simply velocity.

Okay. Then what is instantaneous velocity?
Acceleration is the rate which velocity changes over a time interval, or as you know, $\frac{\Delta V}{\Delta s}$. As for instantaneous velocity, it is, as the name suggests, the velocity on a specific time interval (in which we take $t$ to be infinitely close to $0$). So, for instance, even if there is no acceleration on the movement in question (that is, velocity is constant), you can still determine its instantaneous velocity, but of course, it'll be the same for the entire trajectory, given that there is no acceleration. Do you understand?

PeroK
Homework Helper
Gold Member
Acceleration is the rate which velocity changes over a time interval, or as you know, $\frac{\Delta V}{\Delta s}$. As for instantaneous velocity, it is, as the name suggests, the velocity on a specific time interval (in which we take $t$ to be infinitely close to $0$). So, for instance, even if there is no acceleration on the movement in question (that is, velocity is constant), you can still determine its instantaneous velocity, but of course, it'll be the same for the entire trajectory, given that there is no acceleration. Do you understand?

Velocity is rate of change of displacement, and acceleration is rate of change of velocity.

If you want to talk about average velocity and average acceleration that is different. That requires a time interval.

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