Question 1.1: Here we will do a simple conversion of units. Although there...
Here we will do a simple conversion of units. Although there is no maximum speed limit on the German autobahn, signs in many areas recommend a top speed of 130 km/h. Express this speed in meters per second and in miles per hour.
SET UP We know that 1 km = 1000 m. From Appendix D or the inside front cover, 1 mi = 1.609 km. We also know that 1 h = 60 \min = 60 \times (60 s) = 3600 s.
SOLVE We use these conversion factors with the problem-solving strategy outlined above:
\mathrm{130 km/h=\left(\frac{130 \cancel{km}}{1 \cancel{h}} \right) \left(\frac{1000 m}{1 \cancel{km}} \right) \left(\frac{1\cancel{h}}{3600 s} \right)=36.1 m/s, }
\mathrm{130 km/h=\left(\frac{130 \cancel{km}}{1 h} \right)\left(\frac{1 mi }{1.609 \cancel{km}} \right) = 80.8 mi/h }
REFLECT In physics, speeds are often expressed in meters per second, but in the United States people are used to thinking in miles per hour.
These calculations show that the number of miles per hour is roughly twice the number of meters per second; that is, a speed of 36.1 m/s isn’t very different from 80.8 mi/h.
Practice Problem: Suppose you leave the autobahn and reduce your speed to 55 km/h. What is this speed in m/s and in mi/h? Answer: 55 km/h = 15 m/s = 34 mi/h.