A particle moves according to a law of motion s = RE), t z 0, where t is measured in seconds and s in feet. RE) = 0.01* – 0.060" (a) Find the velocity at time t (in f/s). v(4) = (b) What is the velocity after 2 s? v(2) = /s (c) When is the particle at rest? s (smaller value) |s (larger value)

The table shows the position of a motorcyclist after accelerating from rest. t (seconds) 0 s (feet) 0 4.9 10.6 23.1 (a) Find the average velocity (in ft/s) for each time period. (i) [2, 4] 19.85 (ii) [3, 4] 27.2 (iii) [4, 5] 59.1 1 (iv) [4, 6] 93.8 ft/s ft/s ft/s ft/s 2 3 4 50.3 5 6 109.4 237.9 (b) Plot the points in the table to create a graph of s as a function of t to estimate the instantaneous velocity (in ft/s) when t = 3. (Round your answer to one decimal place.) ft/s

Let H(t) be the cost of heating a building in dollars per hour when the outside temperature is t degrees. (a) What are the units of H'(t) ? -Select- (b) What does the statement H'(32) = -3.60 tell us?. O The cost of heating a building will decrease by approximately $3.60 when the outside temperature increases. O When the outside temperature is 32 degrees, the total cost of heating a building decreases by approximately $3.60. O When the outside temperature increases by 32 degrees, the cost of heating a building will decrease by approximately $3.60 per hour. O The cost of heating a building will be approximately $3.60 per hour more when the outside temperature is 33 degrees instead of 32 degrees. O The cost of heating a building will be approximately $3.60 per hour less when the outside temperature is 33 degrees instead of 32 degrees. (c) If we know that H(32) 14 and H'(32) = -3.60 find the equation of the tangent line to H(t) at t= 32. Use y for the dependent variable and t for the…

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.

At time t20, the acceleration of a particle moving on the x-axis is a(t) =t+sint. At t= 0, the velocity of the particle is -2. For what value t will the velocity of the particle be zero? (A) 1.02 (B) 1.48 (C) 1.85 (D) 2.81 (E) 3.14

(b) S A 1 When is the velocity of the particle positive? When is it negative? When is the particle speeding up? When is it slowing down?