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.
or multiplying both sides by t, d
= Vave 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 vav; and the time of travel by t.
s = vavt
This same basic physical relationship can be written in two other forms, obtained by dividing
both sides of the equation by vav or by t.
How far can a car traveling at a rate of 52 miles per hour travel in 2½ hours?
Using Equation 2-13:
s = vavt
s = (52 miles/hour)(2½ hours)
s = 130 miles