WORD PROBLEMSAlgebraProblemsInvolvingMotionMany algebraic word problems involve fundamental physical relationships. Among the mostcommon are problems involving motion. For example, the definition of speed is distancetraveled divided by the time it takes. or multiplying both sides by t, dV_{ave}distancetimedt= V_{ave} x t. For example, if a car travels at 50 miles per hour for 2 hours, the distance traveledequals (50 mi/hr)(2 hr) or 100 miles. This relationship applies for constant velocity motion only.In practice, it is applied more generally by using an average speed or average rate of travel forthe time involved. The distance traveled is often represented by s; the average speed or averagerate of travel, also called the average velocity, by v_{av}; and the time of travel by t.s = v_{av}t(2-13)This same basic physical relationship can be written in two other forms, obtained by dividingboth sides of the equation by v_{av} or by t.(2-14)tsv_{av}(2-15)v_{av}stExample 1:How far can a car traveling at a rate of 52 miles per hour travel in 2½ hours?Solution:Using Equation 2-13:s = v_{av}ts = (52 miles/hour)(2½ hours)s = 130 milesMA-02 Page 54 Rev. 0

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