Problems Involving Motion:

Many algebraic word problems involve fundamental physical relationships. Among the most common are problems involving motion. For example, the definition of speed is distance traveled divided by the time it takes.  V_ave  = distance/time =d/t or multiplying both sides by t, d = V_ave  x t.  For example, if a car travels at 50 miles per hour for 2 hours, the distance traveled equals (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 for the time involved.  The distance traveled is often represented by s; the average speed or average rate of travel, also called the average velocity, by v_av; and the time of travel by t.

s = v_avt

This similar basic physical relationship can be written in two other forms, acquired by dividing both sides of the equation by v_av or by t.

t = s/v_av

V_av = S/t