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# Derivatives and Rate of Change Word Problems: Motion and Relative Speed

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1.A body has an a equation of motion measured in metres after t seconds such that
s=4t3-14t2+40t+8.

a) When and where is the body momentarily at rest?
b) For what time interval is it moving forward?
c) During what times is its acceleration negative?
d) Draw three separate graphs for acceleration, velocity, and displacement. Explain the relationship between the important information on the graphs.

2.Mrs. Gordon lives on an island 1 km from the mainland. She paddles her canoe at 3km/h and jogs at 5km/h. The nearest drug store is 3 km along the shore from the point on the shore closest to the island. Where should she land to reach the drug store in minimum time?

3.A power boat travels west at 24 km/h. At the instant it passes a buoy, a sailboat sailing north at 7 km/h is 25 km south of the buoy. Calculate the positions of the vessels when there is a minimum distance between them.