Physics: Principles with Applications (7th Edition)

Published by Pearson
ISBN 10: 0-32162-592-7
ISBN 13: 978-0-32162-592-2

Chapter 2 - Describing Motion: Kinematics in One Dimension - General Problems: 65

Answer

(a) The time needed to reach the third stoplight is 14.4 seconds. There is not enough time to make it through all three stoplights without stopping. (b) By 4.6 seconds, the car would not make it through all three stoplights.

Work Step by Step

(a) $v = (40 ~km/h)(\frac{1000 ~m}{1 ~km})(\frac{1 ~h}{3600 ~s}) = 11.1~m/s$ The total distance to the third stoplight is: 10 m + 15 m + 50 m + 15 m + 70 m = 160 meters We can use the distance to the third stoplight to find the required time: $t = \frac{x}{v} = \frac{160 ~m}{11.1 ~m/s} = 14.4 ~s$ The time needed to reach the third stoplight is 14.4 seconds. Since the stoplights are green for 13.0 seconds, there is not enough time to make it through all three stoplights without stopping. (b) The distance from the car to the other side of the intersection after the third stoplight is 165 meters. We can calculate the time of the acceleration period. $t = \frac{v-v_0}{a} = \frac{11.1 ~m/s - 0}{2.00 ~m/s^2} = 5.55 ~s$ In 5.55 seconds, we can calculate how far the car will travel: $x = \frac{1}{2}at^2 = \frac{1}{2}(2.00 ~m/s^2)(5.55 ~s)^2$ $x = 30.8~m$ The car travels 30.8 meters in the first 5.55 seconds. The car still needs to travel 134.2 meters to go through the third intersection. $t = \frac{x}{v} = \frac{134.2 ~m}{11.1 ~m/s} = 12.09~s$ To go through the intersection after the third stoplight, the car needs a total time of 5.55 seconds + 12.09 seconds which is 17.6 seconds. Since the stoplights are green for 13.0 seconds, the car would not be able to make it through all three stoplights. By 4.6 seconds, the car would not make it through all three stoplights.
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