Homework #2

Homework #2 - jiwani(amj566 Homework02 Fouli(58395 This...

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jiwani (amj566) – Homework02 – Fouli – (58395) 1 This print-out should have 17 questions. Multiple-choice questions may continue on the next column or page – fnd all choices be±ore answering. 001 10.0 points A tank holds 1000 gallons o± water, which drains ±rom the bottom o± the tank in hal± an hour. The values in the table t (min) 5 10 15 20 25 30 V (gal) 611 462 205 165 16 0 show the volume, V ( t ), o± water remaining in the tank (in gallons) a±ter t minutes. P is the point (15 , V (15)) on the graph V as a ±unction o± time t , fnd the slope o± the secant line PQ when Q = (25 , V (25)). 1. slope = 25 . 7 2. slope = 40 . 6 3. slope = 37 . 8 4. slope = 18 . 9 correct 5. slope = 4 Explanation: When P = (15 , V (15)) , Q = (25 , V (25)) the slope o± the secant line PQ is given by rise run = V (25) V (15) 25 15 . From the table o± values, there±ore, we see that slope = 16 205 25 15 = 18 . 9 . 002 10.0 points A car frst slows down, but then speeds up. Sketch a graph o± the position o± the car as a ±unction o± time. 1. time position 2. time position 3. time position 4. time position

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jiwani (amj566) – Homework02 – Fouli – (58395) 2 5. time position 6. time position correct Explanation: When the position of the car is plotted against time, the slope of the graph indicates the speed of the car, the greater the slope, the greater the speed, and the car is stationary when the slope is zero. Thus of the graphs, only time position has the given properties. 003 10.0 points The position as a function of time t of a car initially heading due north on IH35 is shown in 2 4 6 2 4 time position List the values of m 1 = average velocity on [3 , 6] , m 2 = instantaneous velocity at t = 3 , m 3 = average velocity on [1 , 2] , m 4 = instantaneous velocity at t = 5 , in increasing order. 1. m 4 , m 1 , m 2 , m 3 correct 2. m 1 , m 2 , m 3 , m 4 3. m 2 , m 3 , m 1 , m 4 4. m 3 , m 4 , m 2 , m 1 5. m 3 , m 1 , m 2 , m 4 6. m 2 , m 1 , m 4 , m 3 Explanation: If s ( t ) denotes the position of the car at time t , then the average velocity over the time interval [ a, b ] is the slope s ( b ) s ( a ) b a
jiwani (amj566) – Homework02 – Fouli – (58395) 3 of the secant line from ( a, s ( a )) to ( b, s ( b )), while the instantaneous velocity at t = a is the slope of the tangent line at the point ( a, s ( a )) on the graph of s . A positive value for the slope indicates that the car is heading north- wards, while a negative value indicates that it is heading southwards. Thus by inspection, instantaneous velocity at t = 5 < average velocity on [3 , 6] < instantaneous velocity at

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This note was uploaded on 07/10/2011 for the course KIN 321M taught by Professor Jensen during the Spring '11 term at University of Texas.

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Homework #2 - jiwani(amj566 Homework02 Fouli(58395 This...

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