If a space shuttle's downward acceleration is given by y"(t) = –32 ft/s², find the osition function y(t). Assume that the shuttle's initial velocity is y'(0) =-100 ft/s nd that its initial position is y(0) = 100,000 ft. Use the position function to find the osition of the shuttle after 5 seconds.

Find the position function of a particle that travels along the x-axis for t >= 0 with acceleration of a(t)=8t-5 where the velocity at t=2 is 6 in/sec and the initial position at time t=0 is -4 inches

Let y(t) be the height (in meters) after time t (in seconds) of a rover that is landing on some other planet with the help of a parachute. Taking into account gravity and air resistance, physicists suggest that the air resistance is proportional to velocity. Further data suggests that the fall can be modeled by y"=-5-3y'. If the parachute is released at a height of 600m with an initial velocity of 0m/s, what is its height after t seconds? What is its terminal velocity? y(t) = The terminal velocity is Submit m/s. m/s

Let C(t) be the daily cost in dollars per day to cool a house when the average outside temperature is t degrees Fahrenheit. What are the units of C'(95)?