Question

# 2. Find the most general antiderivative of the function. (Check your

answer by differentiation. Use C for the constant of the antiderivative.)
f(x)=(9+t+t^2)/(√t)

3. A model rocket is fired vertically upward from rest. Its acceleration for the first three seconds is a(t)=96t at which time the fuel is exhausted and it becomes a freely "falling" body. 19 seconds later, the rocket's parachute opens, and the (downward) velocity slows linearly to −16ft/s in 5 s. The rocket then "floats" to the ground at that rate.

(a) Determine the position function s  and the velocity function v (for all times t).
v(t)= if 0 ≤ t ≤ 3
if 3 &lt; t ≤ 22
if 22 &lt; t ≤ 27
if t &gt; 27

s(t)= if 0 ≤ t ≤ 3
if 3 &lt; t ≤ 22
if 22 &lt; t ≤ 27
if t &gt; 27

15. A high-speed bullet train accelerates and decelerates at the rate of 10ft/s^2. Its maximum cruising speed is 90mi/h. (Round your answers to three decimal places.)

(a) What is the maximum distance the train can travel if it accelerates from rest until it reaches its cruising speed and then runs at that speed for 15 minutes?
?  mi

(b) Suppose that the train starts from rest and must come to a complete stop in 15 minutes. What is the maximum distance it can travel under these conditions?
? mi

(c) Find the minimum time that the train takes to travel between two consecutive stations that are 45 miles apart.
? min

(d) The trip from one station to the next takes at minimum 37.5 minutes. How far apart are the stations?
? mi  