What Formula Do I Use to Find 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!

 

[drpizza]

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.

 

[Iceclover]

i still don't really get it?

 

[drpizza]

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.

Perhaps if you put your question into context, I could help you better.