# Instantaneous velocity formula

• Iceclover
In summary, instantaneous velocity is the rate of change of an object's position at a specific point in time. It can be found using calculus or by taking the final velocity at a given time. In a calculus-based physics course, it is the first derivative of the position function with respect to time. In simpler cases, such as a constant velocity or a falling object, it can be calculated using basic formulas. It is important to consider the context of the problem in order to determine the appropriate method for finding instantaneous velocity.
Iceclover
I was just confused on what formula i use to find instantaneous velocity if anyone can give me an example or explain how i figure it out that would be great. thanks!

Formula? Well, not specifically a formula. However, you understand what instantaneous velocity is, right? It's what the speedometer of the car says (plus the direction the car is traveling.) If the car is traveling at a constant speed, then the instantaneous speed is the same speed throughout the time it's traveling.

If you look at it in a graphical sense; specifically a graph of displacement vs. time, the instantaneous velocity is the rate of change of the curve at any particular point. (Also stated as the slope of the curve, or more correctly, the slope of the tangent line to the curve at a point.) If you're in a calculus based physics course, the instantaneous velocity would be the first derivative of the position function, with respect to time.

i still don't really get it?

If you are using calculus in your physics class, then the instantaneous velocity is the derivative of the displacement function.

If you're not using calculus, then, I suppose, the answer is "it all depends."
For example, if an object starts at 3 m/s, and accelerates at 5 m/s^2 for 8 seconds, and you're wondering what the instantaneous velocity is after 7 seconds, then just treat the 7 second time as when a final velocity occurs. i.e. 3m/s + 5 m/s^2 * 7s = 38m/s

If you throw a ball horizontally at 10 m/s off a cliff, then the horizontal component of velocity will always be 10m/s (til it hits the ground, and as usual, ignoring air resistance.) The vertical component of velocity will be increasing at 9.81 m/s^2. So, after 3 seconds, it's vertical component of velocity will be 3 * 9.81 m/s = 29.43 m/s. You can find the instantaneous velocity at the 3 second point by applying the pythagorean theorem.

If you have a car traveling at a constant velocity of 4 m/s East, then at the 1 second point, 2 second point, and any other point in time while it's moving, the instantaneous velocity is 4m/s East.

## What is the formula for calculating instantaneous velocity?

The formula for calculating instantaneous velocity is v = lim Δt → 0 (Δx/Δt), where v is the instantaneous velocity, Δx is the change in position, and Δt is the change in time.

## How is instantaneous velocity different from average velocity?

Instantaneous velocity is the velocity of an object at a specific moment in time, while average velocity is the total displacement divided by the total time elapsed.

## Can the instantaneous velocity ever be negative?

Yes, the instantaneous velocity can be negative if the object is moving in the opposite direction of its initial motion.

## What is the significance of the limit in the instantaneous velocity formula?

The limit in the formula represents the idea of taking the average velocity over smaller and smaller time intervals, which gives a more accurate measurement of the instantaneous velocity at a specific moment in time.

## How is the instantaneous velocity formula used in real-world scenarios?

The instantaneous velocity formula is used in physics and engineering to calculate the velocity of objects in motion, such as cars, projectiles, and satellites. It is also used in calculus to find the derivative of position with respect to time.

• Introductory Physics Homework Help
Replies
5
Views
1K
• Introductory Physics Homework Help
Replies
7
Views
340
• Introductory Physics Homework Help
Replies
8
Views
657
• Introductory Physics Homework Help
Replies
5
Views
789
• Introductory Physics Homework Help
Replies
4
Views
2K
• Introductory Physics Homework Help
Replies
2
Views
956
• Introductory Physics Homework Help
Replies
5
Views
1K
• Introductory Physics Homework Help
Replies
2
Views
1K
• Introductory Physics Homework Help
Replies
4
Views
915
• Introductory Physics Homework Help
Replies
1
Views
366