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4-79.
1. Compare how distance and velocity are related with these two scenarios: Homework Help ✎

1. As an arrow flies through the air, the distance it has traveled in feet at time t is . Without your calculator, find the velocity, s'(t), at times t = 1, 4, and 16 seconds. Explain what concepts of calculus you applied in order to solve this problem.

2. As a train travels through a station, its velocity, measured in miles per hour, is v(t) = 9t + 32. If the train is in the station when t = 0, determine the position of the train at t = 1 hour. Explain what concepts of calculus you applied in order to solve this problem.

3. Both (a) and (b) involve distance and velocity. However, each required a different method or approach. Describe the relationship between distance and velocity, as well as the derivative and area under a curve.   Three big concepts to choose from are limits, derivatives and integrals. Refer to hint in part (a). Think back to the Freeway Fatality problem 1-1.