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

\begin{tabular}{ c } $t$

(seconds)

& 0 & 10 & 20 & 30 & 40 & 50 & 60 & 70 & 80 \hline

$v(t)$

(feet per second)

& 5 & 14 & 22 & 29 & 35 & 40 & 44 & 47 & 49 \hline \end{tabular}
(a) Find the average acceleration of rocket $A$ over the time interval $0 \leq t \leq 80$ seconds. Indicate units of measure.
(b) Using correct units, explain the meaning of $\int_{10}^{70} v(t)\, dt$ in terms of the rocket's flight. Use a midpoint Riemann sum with 3 subintervals of equal length to approximate $\int_{10}^{70} v(t)\, dt$.
(c) Rocket $B$ is launched upward with an acceleration of $a(t) = \frac{3}{\sqrt{t+1}}$ 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 feet per second. Which of the two rockets is traveling faster at time $t = 80$ seconds? Explain your answer.

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

$t$ (seconds)	0	10	20	30	40	50	60	70	80
$v(t)$ (feet per second)	5	14	22	29	35	40	44	47	49

(a) Find the average acceleration of rocket $A$ over the time interval $0 \leq t \leq 80$ seconds. Indicate units of measure.
(b) Using correct units, explain the meaning of $\int_{10}^{70} v(t)\, dt$ in terms of the rocket's flight. Use a midpoint Riemann sum with 3 subintervals of equal length to approximate $\int_{10}^{70} v(t)\, dt$.
(c) Rocket $B$ is launched upward with an acceleration of $a(t) = \frac{3}{\sqrt{t+1}}$ 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 feet per second. Which of the two rockets is traveling faster at time $t = 80$ seconds? Explain your answer.