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→∞?