A particle moves along a straight line and its position at time t is given by s(t) = 2t3 - 21t2 + 72t, t>0 where s is measured in feet and t in seconds. (A) Use interval notation to indicate the time interval or union of time intervals when the particle is moving forward and backward. .... Forward: Backward: (B) Use interval notation to indicate the time interval(s) when the particle is speeding up and slowing down. ................... Speeding up: Slowing down:

A potato is launched vertically upward with an initial velocity of 170 feet per second from a potato gun at the top of an 66-foot-tall building. The distance in feet that the potato travels from the ground after t seconds is given by s(t) 16+2 + 170t + 66. a) Find the velocity of the potato after 2.2 seconds and 7 seconds. At t = 2.2 seconds, v = At t = 7 seconds, v = feet per second. feet per second. b) Find the speed of the potato at 2.2 second and 7 seconds. At t = 2.2 seconds, the speed of the potato is At t = 7 seconds, the speed of the potato is c) Determine when the potato reaches its maximum height. t seconds Determine how long the potato is in the air. seconds. d) Find the acceleration of the potato at 2.2 seconds and 7 seconds. At t = 2.2 seconds, a = At t = 7 seconds, a = feet per second. Determine the velocity of the potato upon hitting the ground. feet per second. feet per second. feet per second per second. feet per second per second.