Quote of the Day:
"In the beginning (if there was such a thing), God created
 Newton’s laws of motion together with the necessary masses 
 and forces. This is all; everything beyond this follows 
 from the development of appropriate mathematics methods by 
 means of deduction."  -- Albert Einstein

Objectives:
The student will learn to solve problems involving velocity 
  and acceleration.

1. Bellringer 

2. Problem:  
	There is a single path up a mountain in Shenandoah 
	National Park.
	A mountaineer starts up at 7:00 AM and arrives at the
	top at 7:00 PM. She stays there overnight.
	The next morning, she starts back down at 7:00 AM and 
	arrives at the bottom at 7:00 PM.
	On both days, she travels at varying speeds – enjoying 
	the scenery, stopping for lunch, smelling the roses…
	What is the probability that there was a spot on the 
	trail that she passed at exactly the same time on both 
	days?


	Hint: Draw a Displacement – Time graph!

	Answer: It is 100%.  Look at the Displacement-Time 
	Graph – it doesn't matter how long she takes to come 
	back down, there must be at least one place where the 
	descent curve must cross the ascent curve.

3. Given a displacement curve,  s = f(t)
        The velocity is defined to be the change in the 
	displacement divided by the change in time,
	or in other words, the first derivative of 
	displacement with respect to time.
	It measures how fast you are going.
	
	The acceleration is defined to be the change in the 
	velocity divided by the change in time, or in 
	other words, the derivative of velocity with 
	respect to time.
	When you press down on the accelerator in your 
	car, you are changing the velocity.
	
	The jerk is a sudden change in acceleration.  When 
	a ride in a car is jerky, it is not that the 
	accelerations involved are necessarily large but 
	that the changes in acceleration are abrupt.
	Jerk is what spills your soft drink.
	The derivative responsible for jerk is the third 
	derivative of position.

        Example:

4. From physics, we have studied the formula for free fall 
   motion:

5. Example
     Nolan Ryan, one of the fastest pitchers of all-time,
     could throw a baseball 150 ft/sec (over 102 mph).
     Could Nolan Ryan hit the 208-ft ceiling of the Houston
     Astrodome if he were capable of giving a baseball an 
     upward velocity of 100 ft/sec from a height of 7 feet?

     Solution:

7. Examples -- p. 340

    Difference between speed and velocity

    Graphs of displacement -- ask whether velocity is positive or negative,
                              whether acceleration is positive or negative,
                              and whether the particle is slowing down or speeding up.
  
8. How to Live Your Life...  from Alma Barkman

      When Canada's Donovan Bailey ran the one-hundred-meter sprint in 
   9.84 seconds, he was acclaimed as the world's fastest man.
   
      According to an article in the sports section, it almost didn't happen. 
   With so many wins under his belt, Bailey had become overly confident, 
   and before the big race he confessed he found it difficult to accept 
   coaching and apply himself to the rigorous training such a challenge required.  
   But he won the race, and dozens of experts analyzed the tapes in order to 
   ascertian his secret.  The consensus?  He was still accelerating when he
   crossed the finish line.

      This should be an example for us on how to live our lives.  Don't slow
   down as you grow older -- make sure that you are accelerating when you
   cross that finish line!

9. Assignment
     Finish "Class, Take Your Seats!" Worksheet.
     Do p. 342 (1, 4, 7, 13)  

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