Question

How to find instantaneous and average velocity?

Answer 1

Average velocity is equal to the change in distance / change in time :

v(avg) = s / t

that's the average distance, but at some point the object could have moved faster / slower and we want to see the instantaneous velocity. The principal is the same. You take a a little piece of the road for a little piece if time and get the avg velocity of the tiny part of the road. But this way it will be not the exactly speed at that moment, it will be just the avg speed in the little fragment. So we must add limits. What will be the velocity for so tiny part of time that it approaches zero?
We get :

lim s/t = ds/dt
t->0

Answer 2

Instantaneous velocity is found by taking the derivative of the position function with respect to time, giving the velocity at a specific moment. Average velocity is calculated by dividing the total displacement by the total time elapsed.

To find instantaneous velocity, we take the derivative of the position function x(t) with respect to time t. This provides the velocity at any given moment. Mathematically, if the position x is a function of time t, then the instantaneous velocity v at time t is defined as:

v = lim_(Δt→0) (x(t + Δt) - x(t)) / Δt

For average velocity, we simply take the total displacement (the change in position) and divide it by the total time elapsed. Suppose we have an object that moves from position x1 to x2 over a time period from t1 to t2, the average velocity ū is:

ū = (x2 - x1) / (t2 - t1)

When the time interval becomes very small, the average velocity approaches the instantaneous velocity.