Question

The position function of an object is modeld by s(t)=-t²+9t, where t element of [0,9] Determine its velocity and acceleration at the end of the time interval.

Answer 1

To find the velocity and acceleration at the end of the time interval, take the derivative of the position function. The velocity at the end of the time interval is -9 m/s and the acceleration is -2 m/s².

Step-by-step explanation:

To determine the velocity and acceleration at the end of the time interval, we need to find the derivative of the position function. Taking the derivative of s(t) = -t² + 9t with respect to time, we get v(t) = -2t + 9.

The velocity function v(t) = -2t + 9 represents the object's velocity as a function of time. To find the velocity at the end of the time interval, we substitute t = 9 into the velocity function v(t) to get v(9) = -18 + 9 = -9 m/s.

To find the acceleration, we take the derivative of the velocity function. Taking the derivative of v(t) = -2t + 9, we get a(t) = -2. Therefore, the acceleration at the end of the time interval is a(9) = -2 m/s².