A particle moves according to a law of motion s = (t), £ z 0, where t is measured in seconds and s in feet. RE) = 0.01* – 0.06 (a) Find the velocity at time t (in f/s). v(t) = (b) What is the velocity after 2 s? v(2) = (c) When is the particle at rest? s (smaller value) |s (larger value)

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.

A mass of 0.5 kg stretches a spring 0.09 m. The mass is in a medium that exerts a viscous resistance of 34 m N when the mass has a velocity of 4 .. The viscous resistance is proportional to the speed of the object. S Suppose the object is displaced an additional 0.04 m and released. m Find an function to express the object's displacement from the spring's natural position, in m after t seconds. Let positive displacements indicate a stretched spring, and use 9.8 as the acceleration due to s² gravity. u(t)=