Compare how distance and velocity are related with these two scenarios:
A ferry crosses the bay so that its distance (in miles) from the dock at time
is . What is the velocity, , at times , , and hours? Explain what concepts of calculus you applied in order to solve this problem.
. Describe what velocity looks like on a distance graph.
When a cat chases a mouse, the cat’s velocity, measured in feet per second, is
. Sketch a graph and calculate the distance the cat ran in the first seconds. Explain what concepts of calculus you applied in order to solve this problem.
Describe what distance (or displacement) looks like on a velocity graph.
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.