A stone is tossed into the air from ground level with an initial velocity of 30 m/s. Its height at time t is h(t) = 30t – 4.9t² m. Compute the stone's average velocity ū in m/s over the time intervals [2, 2.01], [2, 2.001], [2, 2.0001] and [1.9999, 2], [1.999, 2], [1.99, 2]. (Use decimal notation. Give your answers to three decimal places.)

A rocket will carry a communications satellite into low Earth orbit. Suppose that the thrust during the first 200 sec of fligh is provided by solid rocket boosters at different points during liftoff. The graph shows the acceleration in G-forces (that is acceleration in 9.8-m/sec2 increments) versus time after launch. a. Approximate the interval(s) over which the acceleration is increasing. b. Approximate the interval(s) over which the acceleration is decreasing. c. How many turning points does the graph show? d. Based on the number of turning points, what is the minimum degree of a polynomial function that could be used to model acceleration versus time? Would the leading coefficient be positive or negative? e. Approximate the time when the acceleration was the greatest. f. Approximate the value of the maximum acceleration. Acceleration in G-Forces vs. Time after Liftoff {(184, 2.85), 2.5 2H(12, 1.36)| 1.5 0.5 |(68,0.97)| 40 80 120 160 200 Elapsed Time (sec) Acceleration (G-Forces)

The deck of a bridge is suspended 285 feet above a river. If a pebble falls off the side of the bridge, the height, in feet, of the pebble above the water surface after t seconds is given by  y = 285 − 16t2. (a) Find the average velocity (in ft/s) of the pebble for the time period beginning when t = 2 and lasting the following amount of time. (i) 0.1 seconds  (ii)0.05 seconds  (iii)0.01 seconds  (b) Estimate the instantaneous velocity (in ft/s) of the pebble after 2 seconds.

Suppose A = 500(1.045)t . Compute dA/dt