EXAM 1                September 29, 1995               PHYS 207H
	                                                                               
	      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.  Each
	problem is worth 25 points.
	    
	             2            2                                   -31
	g = 9.8 m/sec  = 32 ft/sec    Mass of the electron = 9.11 x 10   kg
	
	                                                 6             
	                  Radius of the earth = 6.38 x 10  m           
	
	     1.  a.  Sketch a single v-versus-t curve in which there are
	(labelled) points or segments where
	  (1) the acceleration is zero and constant while the velocity is
	not zero,
	  (2) the acceleration is zero but not constant,
	  (3) the velocity and acceleration are both positive,
	  (4) the velocity is positive and the acceleration is negative,
	  (5) the velocity is zero but the acceleration is not.
	
	  State and explain how to remember (not necessarily derive):   
	
	         b.  The relations for the position and velocity of a
	particle as a function of time for motion in one dimension with
	constant acceleration. 
	
	         c.  The relation giving the magnitude of the acceleration
	for a particle moving at constant speed  v  in a circle of radius  R.
	
	     2.  (From homework)  A pitcher throws a fastball at 140 km/h
	toward home plate, which is 18.4 m away.  Neglecting air resistance
	(!), find how far the ball drops because of gravity by the time it
	reaches home plate.
	
	     3.  We have mentioned that the rate of change of acceleration
	is called jerk.  Find the vector giving the jerk for motion at
	constant speed around a circle, with its angle  theta = wt .  In
	your diagram, show the position, velocity, acceleration, and jerk of
	                                         o
	the particle when it is at an angle of 45  above the x-axis.  Hint:
	Start with 
	
	                     ^         ^
	           r(t) = R [x f(wt) + y g(wt)]
	
	with the proper f(wt) and g(wt).
	
	      d                              d
	      -- cos(wt) = -w sin(wt)        -- sin(wt) = w cos(wt)
	      dt                             dt
	   
	
	     4.  A police car is at rest alongside a road monitoring passing
	cars when one passes at a constant speed of 32 m/s.  Five seconds
	later, the police car accelerates from rest with an acceleration of
	       2
	1.6 m/s  .  If it could maintain this acceleration, how far would it
	move before catching the other car?