forces and motion

[...]... different distances, 20 miles and then 20.3 miles along the highway The first location can be symbolized as d i , and the second location can be symbolized as df The subscript i stands for initial, and the sub-­ script f stands for final, another physics convention Putting our different symbols together, we ­have ∆d = ­d f – ­d i = (20.3 – 20) miles = 0.3 ­miles 17 18 forces and motion and ∆t = ­t f – ­ti =... essential ingredi-­ ent to understanding the velocity of a plane that he must pilot In that chapter, we represent vectors both with pictures and in terms of their components, and explore how to do algebra with them We see how displacement, velocity, and acceleration vectors are needed to fully understand interesting motions, and see how a simple accelerometer indicates the strength and direction of ac-­ celeration... t, for the mouse and the jaguar The mouse’s position, xmouse (t) is shown by the dashed line; the jaguar’s, xjaguar (t), by the red ­line 29 30 forces and motion a ­ nswer; it’s one additional thing that they have in common.) But they arrived at the answer in what might seem to be totally differ-­ ent ways Graphs and equations are two useful and complemen-­ tary ways of understanding motion In this chapter... tures that you hold with one hand and flip through its pages with the thumb of the other The images change very gradually from one page to the next page, so that when you flip through it, the 25 26 forces and motion book gives the illusion of motion Maybe this is what the ancient Greek philosopher Parmenides had in mind when he proposed that nothing really ­moves—­that motion is an illusion.7 In the... larger total distance, because it followed the pattern of the New York streets and avenues The distance that the taxi actually covered along the Figure 2.2  The grid of streets (hori-­ zontal) and avenues (vertical) in part of New York ­City 21 22 forces and motion streets and avenues is D = a + b, where a = 20 (1/20) mile and b = 3 (1/5) mile ­So D = 20 (1/20) mile + 3 (1/5) mile = 1.6 ­miles This suggests... on paper, and then isolating smaller and smaller segments of it, a very short segment of a curve looks very much like a straight line Thus ∆d represents the length of that segment in the limit that it is a short, perfectly straight line Thus, the path distance and displacement, D and ∆d, will be ­identical: D = ∆d = δd          in the limit that δt becomes extremely ­small 33 34 forces and motion In... where Lori and her friends are challenged to find out about the g ­ - forces on a roller coaster We explore examples like a geosynchro-­ nous satellite and a plane that must “touch and go” from a runway In Chapter 6, force makes its appearance Ashok and his friends ponder what would happen if, as in a science-fiction film they’ve seen, someone is expelled into outer space The nature of motion in the... fps and have them see the motion as realistic Live-action movies are filmed and shown in theatres at a rate of 24 fps, with motion still looking natural With ­computerg ­ enerated animation, studios like Pixar (The Incredibles) or Dream-­ works Animation SKG (Shrek) combine artistic and mathematical skill in computer programs that, though the final product is still limited to 24 fps, also make motion. .. Oliver took his favorite approach of drawing graphs He drew some axes and labeled the vertical one x and the horizontal one t He drew two curves using these axes and called them x jaguar (t) and x mouse (t) Then he saw where the curves crossed The time, t, where they crossed is when the jaguar and mouse coincided (Figure 3.1) Both Oliver and Olivia got the same, correct answer (They usually both get the... when one is floating in space) is discussed and explained in terms of Newton’s first law Introduction The important concept of ­ center-­of-­mass is introduced as well Pressure forces are explained, and Ashok understands the impor-­ tance of both gravity and atmospheric pressure to keep the human body in healthful ­balance Finally, in Chapter 7, Newton’s second and third laws are pre-­ sented In that . y0 w0 h0" alt="" Forces and Motion PHYSICS IN ACTION Energy Forces and Motion The Nature of Matter Planets, Stars, and Galaxies Processes That Shape the Earth Forces and Motion Amy Bug Series. 46 5 Accelerated Motions . . . . . . . . . . . . . . . . . . . 68 6 Forces: What They Are and What They Do . . . . . . . . . . . . . . . . . . . . . . . . 82 7 Forces and Accelerations. how displacement, velocity, and acceleration vectors are needed to fully understand interesting motions, and see how a simple accelerometer indicates the strength and direction of ac- celeration.