EXAM 1                  October 3, 1990            PS 207                      
                                                                               
If you need a constant not given here or do not understand a                   
problem, please ask me about it.  Remember to include diagrams                 
and explain your reasoning.  No notes, books, etc. may be                      
used during this exam.                                                         
                                                                               
                  2            2                                               
     g = 9.8 m/sec  = 32 ft/sec                                                
                                          -31                                  
     The mass of the electron is 9.11 x 10    kg                               
                                                                               
     1.   (10 points ).  State and explain how to remember  (not               
necessarily derive)                                                            
                                                                               
       (a).  The relation for the position of a particle as a                  
function of time for motion in one dimension with constant                     
acceleration.                                                                  
                                                                               
       (b).  The relation giving the magnitude of the                          
centripetal acceleration for a particle moving at constant speed               
v  in a circle of radius  R.                                                   
                                                                               
                                                                               
      The remaining problems count 30 points each.  A diagram is               
required for each problem.                                                     
                                                                               
                                                                               
      2.  How fast must a ball be rolled along a 70-cm-high table so           
that when it rolls off the edge it will strike the floor at this               
same distance  (70 cm) from the point directly below the table                 
edge?  [If you work this problem algebraically you need not                    
substitute numbers into your answer.]                                          
                                                                               
      3.   (From homework)  A person walks up a stalled escalator in time      
                                                                               
t  .  When standing on the same escalator, now moving, he is                   
 w                                                                             
carried up in time  t  .  How much time  t  would it take him to               
                     e                    B                                    
walk up the moving escalator?                                                  
                                                                               
                                                                               
      4.  A sports car can accelerate uniformly at a rate  a  .  Its           
                                                            1                  
maximum braking deceleration cannot exceed  a  .  What is the                  
                                             2                                 
minimum time required to go a distance  d , assuming that it                   
                                                                               
begins and ends at rest?  [It may help to sketch a graph of                    
                                                                               
velocity vs. time; note that the acceleration and deceleration                 
                                                                               
times need not be the same.  Partial credit will be allowed for                
                                                                               
working the problem with  a  = 0.5g ,  a  = 0.7g , and d = 500 m.]             
                           1            2