# Difference between Instantaneous Velocity and Acceleration?

I'm studying the Speed and Velocity chapter. But there isn't anywhere mentioned in my book about clarity for the exact difference between Instantaneous speed and Acceleration. I'm curious to know about it.

Instantaneous Velocity: Instantaneous Velocity is Changing/Increasing at non-constant rate

Acceleration: Rate of change of velocity is called acceleration

Both terms seem confusing. anyone knows it to explain it in a better way?

The velocity defined as $$\vec{v}=\frac{d\vec{s}}{dt}$$ is called instantaneous velocity. There is also average velocity which equals $$\vec{v}=\frac{\Delta \vec{s}}{\Delta t}$$, over some time $$\Delta t$$. In the case of uniform motion, average velocity over any time is the same as instantaneous velocity at any time.

Uniform motion happens when there is no acceleration on the body.

Instantaneous acceleration is $$\vec{a}=\frac{d\vec{v}}{dt}$$. There is also average acceleration which equals $$\vec{a}=\frac{\Delta \vec{v}}{\Delta t}$$, over some time $$\Delta t$$. In the case of uniformly accelerated motion, acceleration over any time is the same as instantaneous acceleration at any time.

Uniformly accelerated motion happens when a net constant force acts on the body. Hence uniform motion can also be defined as when the body experiences NO net force.

In simple terms, the velocity tells how fast the position is changing whereas the acceleration tells us how fast the velocity is changing.

• Instantaneous means there’s no time involved. So your first equation would be an error with ds/0 Commented Sep 4, 2021 at 8:16
• Instantaneous velocity is the derivative of displacement wrt to time. It is not simply defined as ratio of change in position over time period. Commented Sep 4, 2021 at 8:20
• It may be defined by other things but there’s still time involved and instantaneously infers zero time. Commented Sep 4, 2021 at 8:25
• Velocity is the rate of change in position (the derivative of position to time), $$\vec v=\frac{\mathrm d\vec s}{\mathrm dt}.$$
• Acceleration is the rate of change in velocity (the double derivative of position to time), $$\vec a=\frac{\mathrm d\vec v}{\mathrm dt}=\frac{\mathrm d^2\vec s}{\mathrm dt^2}.$$

Basically, velocity is change in position while acceleration is the change of that change. Your velocity tells how many metres you move each second. So metres-per-second, $$\mathrm{m/s}$$. Your acceleration tells how many more metres-per-second you move with each second. So metres-per-second-per-second, $$\mathrm{m/s^2}$$.

• Yes but what about instantaneous velocity? Commented Sep 4, 2021 at 7:48
• @BillAlsept What I have written in the answer here is instantaneous velocity. Commented Sep 4, 2021 at 9:58