100% + El If we are given a position function: a First Derivative = velocity (speed with a direction) (Rate of Change) 0 Speed would be the absolute value of the first derivative 0 Second Derivative = acceleration (example mphAZ) (Round answers to 2 decimal places if needed) 1.) The position function s(t) = t2 + 51: + 6 represents the height of a stone in feet above the ground as it moves through time in seconds. (For the interval [0,6] Find the average speed of the stone from t=3 tot: 5 At what time did the stone reach its maximum height? Find what time the object hit the ground With what velocity did the stone strike the ground? What was the velocity of the stone after 2 seconds? What is the acceleration of the stone at 3 seconds? At what time is the 2 ft/s? 100% + El 2.) A ball is thrown straight down from the top of a 600 foot building with an initial velocity of -30 feet per second. The function below represents the position function: 5 = 161:2 301: + 600 What is the velocity function? What is the acceleration function? Determine the average velocity of the function on the interval [1,3] Find the instantons velocities when t=1 and t = 3 Find the time that the ball will hit the ground Find the velocity of the ball at impact 100% + El 700 m where 1: IS the 3.) The temperature T (in degrees Fahrenheit) of food in a freezer is T = time in hours. a. Find the rate of change in temperature at 1 hour b. Find the rate of change in temperature at 5 hour c. Find the rate of change in temperature at 10 hour 4.) The ordering and transportation cost C for the components used in manufacturing product is C = 100 (2&0 + \"20) for x 2 1, where C is measured in thousands of dollars and x is the order size in hundreds. a. Find the rate of change with respect to xwhen x = 10 b. Find the rate of change with respect to xwhen x = 20 5.) The price in dollars ofa house during a period of mild ination is described by the formula PU) = 80.00090\