Question

The position function of a ball thrown into the air with a velocity of 23 ft/sec and initial height of 1 foot is given by the function s(t) 16t² +23t +1 where s(t) is the height of the ball above the ground after t seconds. Find the average velocity of the ball on the interval starting with 4 to the time 0.5 seconds later. ate = Problem. Find the average velocity of s(t) =-10t² + 8t + 4 front -4 to t 4 + h.

Answer 1

The average velocity of the ball over the interval from 4 to 4.5 seconds is calculated by using the change in position over the change in time. This requires evaluating the position function at the start and end of the interval and then dividing by the time elapsed.

Step-by-step explanation:

The average velocity of an object is calculated by taking the change in position (Δs) divided by the change in time (Δt). In the scenario given, where a ball is thrown into the air, we need to find the ball's average velocity over a certain interval of time. Given the position function s(t) = -16t² + 23t + 1 and looking at the time interval from 4 to 4.5 seconds, we have:

1. Calculate the initial and final positions: s(4) and s(4.5).
2. Calculate the change in position: Δs = s(4.5) - s(4).
3. Find the time elapsed: Δt = 4.5 - 4 = 0.5 seconds.
4. Divide the change in position by the time elapsed to get the average velocity: Average velocity = Δs / Δt.

By completing these steps, the student will be able to calculate the average velocity over the given time interval.