### Home > CALC > Chapter 4 > Lesson 4.2.2 > Problem 4-58

Compare how distance and velocity are related with these two scenarios: Homework Help ✎A ferry crosses the bay so that its distance (in miles) from the dock at time

*t*is*d*(*t*) = 1 −cos*t*. Find the velocity,*d*′(*t*), at times*t*= 1,*π*, and 5 hours. Explain what concepts of calculus you applied in order to solve this problem.When a cat chases a mouse, the cat's velocity, measured in feet per second, is

*v*(*t*) = 3*t*. Sketch a graph and find the distance the cat ran in the first 5 seconds. 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, mentioning the derivative and area under a curve.

Explain WHY *d* '(*t*) = *v*(*t*). Describe what velocity looks like on a distance graph.

Describe what distance (or displacement) looks like on a velocity graph.