Under what condition is average velocity equal to instantaneous velocity?

Average velocity is defined as the total displacement of an object divided by the total time taken. On the other hand, instantaneous velocity is the velocity of an object at a specific moment in time.

The average velocity is equal to the instantaneous velocity when the object is moving with a constant velocity. In other words, when the object's velocity does not change over time, its average velocity over any time period will be equal to the velocity at any specific moment during that time period. This is because there is no acceleration or change in velocity, so the object's velocity remains constant throughout the entire duration.

To mathematically determine the instantaneous velocity, you can calculate the derivative of the position function with respect to time. By taking the derivative, you can find the velocity function and evaluate it at a specific time to determine the instantaneous velocity.

For example, if the position of an object at time t is given by the function x(t), you can find the velocity function v(t) by taking the derivative of x(t) with respect to t: v(t) = dx(t)/dt. Evaluating v(t) at a specific time t, will give you the instantaneous velocity at that point in time.

So, in summary, the average velocity is equal to the instantaneous velocity when the object has a constant velocity and there is no change in its velocity over time. To find the instantaneous velocity, you can calculate the derivative of the position function with respect to time.