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The Fundamental Theorem of Calculus

The Fundamental Theorem of Calculus

The Fundamental Theorem of Calculus: Position Primed True or False

1. A hummingbird flies away from its feeder with velocity v(t) graphed below.

If the hummingbird is 4 feet from its feeder at time t = 0 seconds, how far is the hummingbird from its feeder at time t = 5 seconds? -> 10 feet

2. A train travels East with velocity v(t) graphed below, where t is measured in hours. On which time interval(s) is the train traveling West?

-> (3, 6) and (9, 12)

3. Ellen goes for an hour drive. Her velocity during this hour is given by the graph v(t) below. What is the fastest speed Ellen attains during her hour-long drive?

-> 50 mph

4. A cheetah's velocity is given by the graph below. At what times does the cheetah change direction?

-> t = 0, 12, 15

5. A cat starts 30 feet up in a tree and continues to climb up the tree with velocity v(t) given by the graph below.

After 10 seconds, how high in the tree is the cat? -> 48 ft

6. A racing snail has velocity given by the graph below. On what intervals is the snail slowing down?

-> (1.5, 3), (4.5, 6), (7.5, 9), (10.5, 12), (13.5, 15)

7. A cheetah is playing by running back and forth with velocity v(t) given by the graph below. Positive velocities indicate the cheetah is running North.

After 5 seconds of running, how far is the cheetah from where it started? -> 0 ft

8. The function v(t) is graphed below. Find .

-> 32

9. The function v(t) is a velocity function on the time interval [a, b]. Select the best interpretation of the integral . -> The area of the velocity function on [a, b].
10. Assume that s(t) is a position function with velocity v(t) = s'(t) on the interval [a, b]. Which of the following statements is true? ->