Author: admin
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Adding Vectors by Components
Using a sketch, we can add vectors geometrically. On a vector-capable calculator, we can add them directly on the screen. A third way to add vectors is to combine their components axis by axis, which is the way we examine here. To start, consider the statement which says that the vector is the same as the…
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Unit Vectors
A unit vector is a vector that has a magnitude of exactly 1 and points in a particular direction. It lacks both dimension and unit. Its sole purpose is to point— that is, to specify a direction. The unit vectors in the positive directions of the x, y, and z axes are labeled , , and , where the hat ^ is used instead…
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Components of Vectors
Adding vectors geometrically can be tedious. A neater and easier technique involves algebra but requires that the vectors be placed on a rectangular coordinate system. The x and y axes are usually drawn in the plane of the page, as shown in Fig. 3-8a. The z axis comes directly out of the page at the origin; we ignore it for now and…
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Adding Vectors Geometrically
Suppose that, as in the vector diagram of Fig. 3-2a, a particle moves from A to B and then later from B to C. We can represent its overall displacement (no matter what its actual path) with two successive displacement vectors, AB and BC. The net displacement of these two displacements is a single displacement from A to C. We call AC the vector sum (or resultant) of the vectors AB and BC. This sum is not the usual…
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Vectors and Scalars
A particle moving along a straight line can move in only two directions. We can take its motion to be positive in one of these directions and negative in the other. For a particle moving in three dimensions, however, a plus sign or minus sign is no longer enough to indicate a direction. Instead, we…
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What Is Physics?
Physics deals with a great many quantities that have both size and direction, and it needs a special mathematical language—the language of vectors—to describe those quantities. This language is also used in engineering, the other sciences, and even in common speech. If you have ever given directions such as “Go five blocks down this street…
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Constant Acceleration: A Special Case
In many types of motion, the acceleration is either constant or approximately so. For example, you might accelerate a car at an approximately constant rate when a traffic light turns from red to green. Then graphs of your position, velocity, and acceleration would resemble those in Fig. 2-8. (Note that a(t) in Fig. 2-8c is constant, which requires that ν(t)…
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Acceleration
When a particle’s velocity changes, the particle is said to undergo acceleration (or to accelerate). For motion along an axis, the average acceleration aavg over a time interval Δt is where the particle has velocity ν1 at time t1 and then velocity ν2 at time t2. The instantaneous acceleration (or simply acceleration) is the derivative of the velocity with respect to time: In words, the acceleration of a particle at any…
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Instantaneous Velocity and Speed
You have now seen two ways to describe how fast something moves: average velocity and average speed, both of which are measured over a time interval Δt. However, the phrase “how fast” more commonly refers to how fast a particle is moving at a given instant—its instantaneous velocity (or simply velocity) ν. The velocity at any instant is obtained…
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Average Velocity and Average Speed
A compact way to describe position is with a graph of position x plotted as a function of time t—a graph of x(t). (The notation x(t) represents a function x of t, not the product x times t.) As a simple example, Fig. 2-2 shows the position function x(t) for a stationary armadillo (which we treat as a particle) over a 7 s time interval. The animal’s position stays…