Final answer:
The velocity of an object at time t=9 seconds, given the position function s(t) = 1296 - 16t², is calculated by differentiating the position function to get the velocity function v(t) = -32t. Substituting t=9 gives a velocity of -288 meters per second.
Step-by-step explanation:
To find the velocity of an object at a specific time when given its position function, you need to take the derivative of the position function with respect to time. The position function given is s(t) = 1296 - 16t². The derivative of this function, s'(t) or v(t), which represents the velocity, is -32t.
Thus, to find the velocity at t=9 seconds, we substitute t with 9 into the velocity function:
v(9) = -32(9) = -288 m/s
The velocity at t=9 seconds is -288 meters per second, indicating the object is moving in the opposite direction of the positive position axis at this time.