48 KINEMATICS. [96. 



ping) B at 9 h. 31 m., C at 9 h. 47 m., and arrives at D at 9 h. 59 m., 

 the distance AD being 36.9 miles. Considering the motion as uniform : 



(a) What is the velocity? 



() What is the equation of motion? 



(c) What are the distances BD and CD? 



(d) If after stopping 5 minutes at D the train goes on with the same| 

 velocity as before, when will it reach , loj miles beyond D? 



(e) Construct a graphical time-table, taking the times as abscissas and ] 

 the distances as ordi nates. 



(2) Interpret equations (i f ) and (i") geometrically. 



(3) A train leaves Detroit at 9 h. 5 m. A.M. and reaches Chicago . 

 at 4 h. 30 m. P.M. ; another train leaves Chicago at 1 2 h. 20 m. and 

 arrives in Detroit at 7 h. 25 m. P.M. The distance is 285 miles. Re-] 

 garding the motion as uniform and neglecting the stops, find, both] 

 analytically and graphically, when and where the trains will meet. 



(4) Reduce the following velocities to F. P. S. units : (a) Walking 4 \ 

 miles an hour; (3) trotting a mile in 2 m. 10 s. ; (c) railroad train,] 

 from 30 to 50 miles per hour; (^/) bicyclist, 2 miles in 4 m. 59^ s. ; 

 (f) sound in air, 333 metres per second. 



(5) What is the numerical value of a velocity of 22 ft. per second 

 when the hour is taken as unit of time and the mile as the unit of 

 length? 



(6) How is the unit of velocity changed if the minute be adopted as 

 unit of time, the unit of length remaining unchanged ? 



(7) The mean distance of the sun being 92 J million miles, what is the 

 velocity of light if it takes light 16 m. 40 s. to cross the earth's orbit? 



(8) Two trains are running on the same track at the rate of 25 and 

 15 miles per hour, respectively. If at a certain instant they are 10 

 miles apart, find when they will collide (a) if they are headed the same 

 way ; (6) if they run in opposite directions. 



(9) In what latitude is a bullet shot west with a velocity of 1320 ft. 

 per second at rest relatively to the earth's axis, the radius being taken 

 as 4000 miles ? 



(10) Two trains, one 250, the other 440 ft. long, pass each other on 

 parallel tracks in opposite directions with equal velocity. A passenger 

 in the shorter train observes that it takes the longer train just 4 seconds 

 to pass him. What is the velocity? 



