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4-79.

Compare how distance and velocity are related with these two scenarios:

1. As an arrow flies through the air, the distance it has traveled in feet at time t is $s ( t ) = 4 \sqrt { t }$. Without your calculator, find the velocity, $s^\prime(t)$, at times $t = 1, 4,$ and $16$ seconds. Explain what concepts of calculus you applied in order to solve this problem.

Three big concepts to choose from are limits, derivatives and integrals.

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.

Refer to hint in part (a).

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.

Think back to the Freeway Fatality problem 1-1.  