The position of a ball as a function of time is given by the function below where
Use your calculator to approximate the instantaneous velocity of the ball at
Instantaneous velocity = Instantaneous Rate of Change (IROC) = Derivative
using the Power rule.
, , and .
What do you predict happens to the velocity of the ball after a very long time (i.e. as
seconds is a very long time for a ball to be in motion. (This must be an unearthly situation!) Is increasing, decreasing or neither as ? Is changing 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
) have a horizontal asymptote as ?