ACCELERATION 



13 



3. A train comes to rest after the brakes have been applied for ten seconds. 

 If the retardation was 8 feet per second per second, what was the velocity of 

 the train when the brakes were first drawn ? 



4. How long does it take a body starting with a velocity of 22 feet per second 

 and moving with an acceleration of 6 feet per second per second, to acquire a 

 velocity of 60 miles an hour ? 



5. Two bodies start at the same instant with velocities u and v respectively; 

 the motion of the first undergoes a retardation of / feet per second per second, 

 while that of the second is uniform. How far will the second have gone by the 

 time that the first comes to rest ? 



6. A body starting from rest moves for 4 seconds with a uniform accelera- 

 tion of 8 feet per second per second. If the acceleration then ceases, how far 

 will the body move in the next 5 seconds ? 



7. A train has its speed reduced from 40 miles an hour to 30 miles an hour 

 in 5 seconds. If the retardation be uniform, for how much longer will it travel 

 before coming to rest ? 



8. A body falling under gravity has an acceleration of 32.2 feet per second 

 per second. Express this acceleration when the units are (a) centimeter, 

 second ; (6) mile, hour. 



12. Parallelogram of accelerations. THEOREM. Let the velocity 

 of a point be compounded of two velocities v^, v z along given direc- 

 tions, and let these velocities be variable, their accelerations being 

 fi> /2- Then if two lines be drawn in the direction of the velocities, 

 to represent f lt f z on any scale, the resultant acceleration will be 

 represented on the same scale ~by the diagonal of the parallelogram 

 of which these , 



lines are edges. 

 To prove the 

 theorem, we 

 consider the 

 motion dur- 

 ing any small 

 interval dt 

 at which the 

 component ac- 

 celerations are 



/!, / 2 . In fig. 7 let AB, AC represent the two velocities v lt v 2 at the 

 beginning of this interval. Let BB f , CC f represent, on the same 

 scale, the infinitesimal increments in velocity in the interval dt, 



FlQ. 1 



