A driver accelerates when the car is traveling at a speed of 30 miles per hour (i.e., 44 feet per second). The velocity (in feet per second) function is v(t)=44+2.2t. The car reaches the speed of 60 miles per hour (i.e., 88 feet per second) in 20 seconds. Then during the 20 seconds the car has traveled miles.

An object is tossed vertically upward from ground level. Its height  s(t),  in feet, at time t seconds is given by the position function  s = −16t2 + 112t. In how many seconds does the object return to the point from which it was thrown?

If a bullet from a pistol is fired straight up from the ground, its height t seconds after it is fired will be s (t) = -16t2 + 1280t feet (neglecting air resistance).  a. Find the velocity function b. How long will it take the bullet to fall back to the ground? c. With what velocity will the bullet hit the ground?

During Ricardo noticed an ink stain with a diameter of about 3 cm on the front of his teacher’s shirt. He then noticed that there was a pen in the pocket and that the ink blot was continuing to spread across the front of the teacher’s shirt. He estimated that the diameter of the ink blot seemed to be growing by about 0.5 cm every 2 minutes. a) Write an equation for the RADIUS, r, of the ink stain, as a function of time, t. Assume that t = 0 represents the time that Ricardo first noticed the ink stain. b) Write an equation showing the AREA, A, of the ink stain as a function of the time t. (Hint: It might help to first write A as a function of r. ) c) Draw a graph of the function A(t) for 10 minutes. d) At what time is the area of the ink stain about 25 square centimeter? Show how you answer this question. (i.e. ”I found it using desmos” is not sufficient)