A car going at 30 ft/sec decelerates at a constant 5 ft/sec2.(a) Draw up a table showing

Chapter 6, Problem 84

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A car going at 30 ft/sec decelerates at a constant 5 ft/sec2.(a) Draw up a table showing the velocity of the car everyhalf second. When does the car come to rest?(b) Using your table, find left and right sums which estimatethe total distance traveled before the car comesto rest. Which is an overestimate, and which is anunderestimate?(c) Sketch a graph of velocity against time. On thegraph, show an area representing the distance traveledbefore the car comes to rest. Use the graph tocalculate this distance.(d) Now find a formula for the velocity of the car as afunction of time, and then find the total distance traveledby antidifferentiation. What is the relationshipbetween your answer to parts (c) and (d) and yourestimates in part (b)?