VELOCITY 7 



as unit of length and the second as unit of time. We can find the 

 amount of this same velocity in other units by a simple proportion. 



Thus suppose it is required to express a velocity of a feet per second 

 in terms of miles and hours. 



The point moves a feet in one second, and therefore a x 60 x 60 feet in 

 one hour, and therefore 



a x 60 x 60 15 a 



3 x 1760 22 



miles 



in one hour. Thus the velocity is one of miles per hour. 



EXAMPLES 



1. A railway train travels a distance of 918 miles in 18 hours. What is its 

 average velocity in feet per second ? 



2. Compare the velocities of a train and an automobile which move uni- 

 formly, the former covering 100 feet a second and the latter 1500 yards a minute. 



3. A man runs 100 yards in 9| seconds. What is his average speed in miles 

 per hour ? 



4. The two hands of a town clock are 10 and 7 feet long. Find the velocities 

 of their extremities. 



5. Taking the diameter of the earth as 7927 miles, what is the velocity in 

 foot-second units of a man standing at the equator (in consequence of the daily 

 revolution of the earth about its axis) ? 



6. Two trains 230 and 440 feet long respectively pass each other on parallel 

 tracks, the former moving with twice the speed of the latter. A passenger in 

 the shorter train observes that it takes the longer train three seconds to pass 

 him. Find the velocities of both trains. 



9. Composition of velocities. All motion, as we have seen, must 

 be measured relatively to a frame of reference. Thus velocity, 

 or rate of motion, must also be measured relatively to a frame 

 of reference. A point may have a certain velocity relative to a 

 frame of reference, while the frame of reference itself has another 

 velocity relative to a second frame. It may be necessary to find 

 the velocity of the moving point with reference to the second 

 frame, in other words, to compound the two velocities. 



To do this we consider the motions which take place during 

 an infinitesimal interval of time dt. Let the moving point have 

 a velocity v^ in a direction AB relative to the first frame, while 



