## Chapter 1 – Excerpt 2

The next excerpt from Chapter 1 discusses velocity, acceleration and force. It contains algebra and calculus (which you may skip), a photo of one of my cats engaged in their other favorite activity (which you may dwell on to make up for skipping the math), and an exposé of the real source of Newton’s discovery of gravity under the apple tree.

As you can tell, cats are allowed on the table at our house. It would be too hard to explain to them that the tabletop is off-limits to cats when they see so many miniature statues of themselves there. Besides, it’s a fertile source of material for scientific investigation.

displacement with respect to time. Just as displacement is a vector and distance is its magnitude, velocity is a vector quantity and speed is the scalar quantity equal to its magnitude. Even for one- dimensional motion, velocity is considered a vector. For example, if an object is traveling at 10 m/s and then reverses direction and goes back at 10 m/s, its new velocity is the negative of what it had been, but its speed is the same. Speed is always nonnegative, since it is a length of a vector. As a mnemonic device, since velocity is the canonical example of a vector, and speed is the Q. Suppose your person rushes you to a veterinarian at 60 miles per hour (mph) and then drives home A. Your average speed is 40 mph, since However, the question was about average Q. This exercise is taken verbatim from a college-level calculus-based physics textbook
Q. Suppose you are chasing a mouse who is traveling at 3 m/s and is initially 20 meters away from you. Your motion is described by x = t
So it takes 5 seconds for you to pounce on the mouse. Now we obtain the velocity function by differentiating the position function: v(t) = dx/dt = d/dt(t
Q. Suppose you are chasing a mouse who is traveling at 3 m/s and is initially 20 meters away from you. You are going faster than the mouse but decelerating, in such a way that every second the distance between yourself and the mouse is halved. Thus, at time t = 1 second, the mouse is 10 meters ahead of you; at t = 2 seconds, you’re only 5 meters apart; and so on. Will you ever reach the mouse and, if so, when? A. This exercise is an example of Zeno’s Paradox. You will only reach the mouse in the limit t → ∞. However, as an engineer would say, when you are within a distance comparable to the width of an atom, you’re certainly "close enough for practical purposes". It is precisely because of such issues involving limits that Newton and Spitface developed the calculus, which allowed us to solve the previous exercise.
Although those three quantities – position, its time derivative velocity, and its second time derivative acceleration – suffice for most applications, an infinitely curious cat may wonder, what about the rest of the infinitely many higher derivatives of position? Actually, the third time derivative of position,
Force, Mass and Gravity A A force of nature is one that exists in the natural world without any action on the part of a human or feline or machine, The discovery of gravity has been attributed to Isaac Newton, in the apocryphal falling apple story, but the credit is actually due to his cat, Spitface. As the story goes, Newton was sitting under an apple tree when an apple fell on his head, and this incident caused him to realize that there was a force pulling the apple to the earth, namely the gravitational attraction between the earth and the apple. However, when analyzing this incident, most people have failed to ask why Isaac was sitting under the apple tree in the first place that fateful day. The answer is that he was very tired and wanted to rest, but when he went to his usual resting place, his favorite overstuffed chair in the living room, Spitface was curled up on it. Had the cat foolishly chosen to sleep in a less comfortable and less safe spot, such as, for example, under the apple tree, Isaac would have rested in his chair that day, as usual, remaining blissfully unaware of the force of gravity. The SI unit of force is called a Newton (abbreviated N). Perhaps the historical oversight is not so unfortunate after all: not only would calling it a Spitface sound ludicrous, but abbreviating it as ‘S’ would lead to confusion with the abbreviation ‘s’ for seconds.
5 – Exercises 23 & 40 on pages 63-64 in 6 – math.ucr.edu/home/baez/physics/General/jerk.html<return-to-text> © All Contents Copyright 2008-2010, Skona Brittain |
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