### Home > CALC > Chapter 4 > Lesson 4.2.3 > Problem 4-79

Compare how distance and velocity are related with these two scenarios: Homework Help ✎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.As a train travels through a station, its velocity, measured in miles per hour, is

*v*(*t*) = 9*t*+ 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.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.