Table given:

Rocket A has positive velocity v(t) after being launched upward from an initial height of 0 feet at time $\displaystyle t=0$ seconds. The velocity of the rocket is recorded for selected values of $\displaystyle t$ over the integral $\displaystyle 0 \leq t \leq 80$ seconds, as shown in the table above.

a. Find the average acceleration of rocket A over the time interval $\displaystyle 0 \leq t \leq 80$ seconds.

b. Explain the meaning of $\displaystyle \int_{10}^{70} {v(t)dt}$ in terms of the rocket's flight. Use a midpoint Riemann sum with 3 subintervals of equal length to approximate $\displaystyle \int_{10}^{70} {v(t)dt}$.

c. Rocket B is launched upward with an acceleration of $\displaystyle a(t) = \frac{3}{\sqrt{t+1}}$ feet per second per second. At time $\displaystyle t=0$ seconds, the initial height of the rocket is 0 feet, and the initial velocity is 2 feet per second. Which of the two rockets is traveling faster at time $\displaystyle t=80$ seconds? Explain.

Thanks a lot to anyone who can help on this!