How to Solve Calculus Word Problems Involving Rockets and Velocity?

[jimjimmonk]

hey guys, can anyone here help me with this problem?
"Rocket A has positive velocity v(t) after being launched upward from an initial height of 0 feet at t=0 seconds. The velocity of the rocket is recorded for selected values of t over the interval 0 <(or = to) t <(or = to) 80 seconds, as shown in the table below.

t (seconds) 0 10 20 30 40 50 60 70 80
v(t) ft/sec 5 14 22 29 35 40 44 47 49

a) Find the average acceleration of rocket A over the time interval 0 <(or = to) t <(or = to) 80 . Indicate units of measure.

b) using correct units, explain the meaning of "the integral of 10 to 70 of v(t)dt" in terms of the rocket's flight. Use a midpoint Riemann sum with 3 subintervals of equal length to approximate "the integral of 10 to 70 of v(t)dt".

c) Rocket B is launched upward with an acceleration of a(t) = 3/sq root(t + 1) feet per second per second. At time t = 0 seconds, the initial height of the rocket is 0 feet, and the initial velocity is 2 ft / second. Which of the 2 rockets is traveling faster at time t = 80 seconds? explain your answer."

I got this problem in class a few days ago and had the whole period to work on it but I was only able to figure out part a:
((ending velocity)-(initial velocity))/(time passed)=((49)-(5))/(80)=(44)/(80)=11/20

Part B completely confuses me so that would be a huge help if someone could help me with that.

And I think I understand how to do part C, I just didn't want to skip b. But you would just integrate "a(t)=3/sq root(t + 1)" to change it to velocity and plug in t=80 and find out which one has a higher velocity at 80 seconds correct?

 

[foxjwill]

For b), you're being asked
1) to explain what is meant by $$\int^{70}_{10} v(t)dt$$
2) to approximate said integral.

Were you confused by them asking for part 1 in terms of the rocket's flight? If so, just ignore that part of the question. It's redundant.

Your method for part c) is correct.