HW02.pdf

# HW02.pdf - young(toy68 HW02 villafuerte altu(53780 This...

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young (toy68) – HW02 – villafuerte altu – (53780) 1 This print-out should have 22 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0points The position of a car as a function of time is given by the values in table t (seconds) 0 1 2 3 4 5 s (feet) 0 18 28 32 50 60 Find the average velocity for the time period beginning when t = 2 and lasting 2 seconds. 1. average vel. = 7 feet/sec 2. average vel. = 9 feet/sec 3. average vel. = 11 feet/sec correct 4. average vel. = 8 feet/sec 5. average vel. = 10 feet/sec Explanation: Average velocity between times t = 2 and t = 2 + h is given by dist. travelled time taken = s (2 + h ) s (2) h . When h = 2, therefore, s (2 + 2) s (2) 2 = s (4) s (2) 2 = 50 28 2 . Consequently, over the time interval from t = 2 to t = 4 the car has average velocity = 11 ft/sec . 002 10.0points A car first speeds up, but then slows down. Sketch a graph of the position of the car as a function of time. 1. time position 2. time position 3. time position correct 4. time position

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young (toy68) – HW02 – villafuerte altu – (53780) 2 5. time position 6. time position 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 10.0points 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 [1 , 2] , m 2 = instantaneous velocity at t = 3 , m 3 = instantaneous velocity at t = 5 , m 4 = average velocity on [3 , 6] , in increasing order. 1. m 3 < m 1 < m 2 < m 4 2. m 1 < m 2 < m 3 < m 4 3. m 4 < m 1 < m 2 < m 3 4. m 2 < m 1 < m 4 < m 3 5. m 2 < m 3 < m 1 < m 4 6. m 3 < m 4 < m 2 < m 1 correct 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
young (toy68) – HW02 – villafuerte altu – (53780) 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 t = 4 < average velocity on [1 , 2] . For the given values of m 1 , ..., m 4 , therefore, m 3 < m 4 < m 2 < m 1 . keywords: position v. time graph, instanta- neous velocity, average velocity, 004 10.0points For the points on the graph of f in A B D C arrange the values of m 1 = 0 , m 2 = 2 , m 3 = slope at D, m 4 = slope at A, as a set of inequalities in descending order when the dashed line is the graph of y = 5 2 x.

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