### Home > CALC > 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

*s*(*t*) is in meters and*t*is in seconds. Homework Help ✎

Use your calculator to approximate the instantaneous velocity of the ball at 1, 5, 10, and 100 seconds.

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

*t*→∞)?What happens to the position of the ball after a very long time, (i.e. what is

*s*(*t*))? Does this make sense given your answer to part (b)?

Instantaneous velocity = Instantaneous Rate of Change (IROC) = Derivative

Find *s*'(*t*) using the Power rule.

Evaluate *s*'(1), *s*'(5), *s*'(10) and *s*'(100).

Note: *t* = 100 seconds is a very long time for a ball to be in motion. (This must be an unearthly situation!) Is *s*(*t*) increasing, decreasing or neither as *t*→∞? Is *s*(*t*) changing rapidly or not so rapidly? Explain.

Does a square root function (such as *s*(*t*)) have a horizontal asymptote as *t*→∞?