A70 APPENDIX Review Physics: Uniform Motion Tanya, who is a long-distance runner, runs at an average speed of 8 miles per hour (mi/h).Two hours after Tanya leaves your house, you leave in your Honda and follow the same route. If your average speed is 40 mi/h, how long is it before you catch up to Tanya? How far are each of you from your home? Solution EXAMPLE 5 Refer to Figure 29.We use t to represent the time (in hours) that it takes you to catch up to Tanya.When this occurs, the total time elapsed for Tanya is + t 2 hours because she left 2 hours earlier. Set up the following table: Rate (mi/h) Time (h) Distance (mi) Tanya 8 + t 2 ( ) + t 8 2 Honda 40 t t 40 The distance traveled is the same for both, which leads to the equation ( ) + = + = = = t t t t t t 8 2 40 8 16 40 32 16 1 2 hour It takes you 1 2 hour to catch up to Tanya. Each of you has gone 20 miles. Check: In 2.5 hours, Tanya travels a distance of ⋅ = 2.5 8 20 miles. In 1 2 hour, you travel a distance of ⋅ = 1 2 40 20 miles. Time t 2 h t = 0 Time t t = 0 Figure 29 Uniform Motion Formula If an object moves at an average speed (rate) r , the distance d covered in time t is given by the formula = d rt (2) That is, = ⋅ Distance Rate Time. 4 Solve Uniform Motion Problems Objects that move at a constant speed are said to be in uniform motion . When the average speed of an object is known, it can be interpreted as that object’s constant speed. For example, a bicyclist traveling at an average speed of 25 miles per hour can be modeled as being in uniform motion with a constant speed of 25 miles per hour.
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