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p02_005

# Fundamentals of Physics,Vol 1 (Chapters 1 - 20)

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5. (a) Denoting the travel time and distance from San Antonio to Houston as T and D , respectively, the average speed is s avg 1 = D T = (55 km / h) T 2 + (90 km / h) T 2 T = 72 . 5 km / h which should be rounded to 73 km/h. (b) Using the fact that time = distance/speed while the speed is constant, we find s avg 2 = D T = D D/ 2 55 km / h + D/ 2 90 km / h = 68 . 3 km / h which should be rounded to 68 km/h. (c) The total distance traveled (2 D ) must not be confused with the net displacement (zero). We obtain for the two-way trip s avg = 2 D D 72 . 5 km / h + D 68 . 3 km / h = 70 km / h . (d) Since the net displacement vanishes, the average velocity for the trip in its entirety is zero. (e) In asking for a sketch , the problem is allowing the student to arbitrarily set the distance D (the intent
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Unformatted text preview: is not to make the student go to an Atlas to look it up); the student can just as easily arbitrarily set T instead of D , as will be clear in the following discussion. In the interest of saving space, we brieﬂy describe the graph (with kilometers-per-hour understood for the slopes): two contiguous line segments, the Frst having a slope of 55 and connecting the origin to ( t 1 , x 1 ) = ( T/ 2 , 55 T/ 2) and the second having a slope of 90 and connecting ( t 1 , x 1 ) to ( T, D ) where D = (55 + 90) T/ 2. The average velocity, from the graphical point of view, is the slope of a line drawn from the origin to ( T, D )....
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