The velocity v (in feet per second) of a rock dropped into a well is related to time (in seconds) by the formula v = 32t. What is the velocity of the rock at the indicated instant? Write your answer in the form (t, v).
(a) when the rock is released
( , )
(b) after 9 seconds
To find the velocity of the rock at the indicated instant, we can use the formula v = 32t, where v represents the velocity and t represents time.
(a) When the rock is released, we can substitute t = 0 into the equation to find the velocity. Therefore, v = 32(0) = 0. So the velocity of the rock when it is released is (0, 0).
(b) After 9 seconds, we can substitute t = 9 into the equation to find the velocity. Therefore, v = 32(9) = 288. So the velocity of the rock after 9 seconds is (9, 288).