A potato is launched vertically upward with an initial velocity of 123 ft/s from a potato gun at the top of an 85-foot-tall building. The distance in feet that the potato travels from the ground after t seconds is given by s(t) = -81t? + 225t +3. %3D (i) Find the velocity of the potato after 0.5 s = ft/s (ii) Find the speed of the potato at 0.5 s = ft/s S (iii) Determine when the potato reaches its maximum heightD (iv) Find the acceleration of the potato at 0.5 s . ft/s?

Find the slope ofthe line in Figure l.

The half-life of plutonium-244 is 80,000,000 years. Find function gives the amount of carbon-14 remaining as a function of time, measured in years.

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.

You peer around a corner. A velocity raptor 64 meters away spots you. You run away at a speed of 6 meters per second. The raptor chases, running towards the corner you just left at a speed of {\displaystyle 4t}4t meters per second (time {\displaystyle t}t measured in seconds after spotting). After you have run 4 seconds the raptor is 32 meters from the corner. At this time, how fast is death approaching your soon to be mangled flesh? That is, what is the rate of change in the distance between you and the raptor?