### Home > CALC > Chapter Ch3 > Lesson 3.2.3 > Problem 3-78

3-78.

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*→∞?