1. Part (a)
Since acceleration is the derivative of velocity, and derivatives are slopes, they’re simply asking for the slope between (0,5) and (80, 49).
Average acceleration =
49 - 5
80 - 0
ft/sec2 =

2. These are the “midpoint Riemann sums”.
Part (b) 10 70
v(t) dt would represent the total distance traveled by the rocket between t= and t=70 seconds after launch.
20 ( ) = 2,020 feet v t 20 40 60 80 50 30 10 70
(20,22)
(40,35)
(60,44)
These are the “midpoint Riemann sums”.
Common rectangle width = 20

3. At t=80 seconds, Rocket B is faster.
Part (c)
v(t) = 6 (t+1) - 4
1/2
v(t) = (t+1) dt
-1/2
v(80) = 6 (80+1) - 4
v(t) = 6 (t+1) + C
1/2
2 = 6 (0+1) + C
1/2
C = -4
v(80) = 50 ft/sec
Rocket A: 49 ft/sec
Rocket B: 50 ft/sec
At t=80 seconds, Rocket B is faster.