A stone is tossed into the air from ground level with an initial velocity of 31 m/s. Its height at time t is  h(t) = 31t − 4.9t2  m. Compute the stone's average velocity over the time intervals  [2, 2.01], [2, 2.001], [2, 2.0001],  and  [1.99, 2], [1.999, 2], [1.9999, 2].  (Round your answers to three decimal places.) and Estimate the instantaneous velocity v at  t = 2

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.

An object with initial temperature 80°C is brought into a 18°C room. At noon the object's temperature was 70°c and 65°C half hour later. (a) When was the object brought into the room? (b) Find the average temperature of the object before 12:30 PM. That is, the average temperature over the time interval measured since the object was brought into the room until half past noon.

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