### Home > APCALC > Chapter 3 > Lesson 3.2.3 > Problem 3-78

The position of a ball as a function of time is given by the function below where is in meters and

*is in seconds.*

Use your calculator to approximate the instantaneous velocity of the ball at

and seconds. Instantaneous velocity = Instantaneous Rate of Change (IROC) = Derivative

Rewrite

using exponents:Find

using the Power rule.Evaluate

and.What happens to the velocity of the ball after a very long time (i.e. as

)?Note:

seconds is a very long time for a ball to be in motion. (This must be an unearthly situation!) Isincreasing, decreasing or neither as? Ischanging rapidly or not so rapidly? Explain.What happens to the position of the ball after a very long time, (i.e. what is)? Does this make sense given your answer to part (b)?

Does a square root function (such as

*s*(*t*)) have a horizontal asymptote as*t*→∞?