Chapter Three Motion in One Dimension Dr. Mukhlis M. Ismail1Fig. 2.1 Chapter Three Motion in One Dimension 2-1 Motion Everything in the world moves. Even seemingly stationary things, such as a roadway, move with Earth's rotation, Earth's orbit around the Sun, the Sun's orbit around the center of the Milky Way galaxy, and that galaxy's migration relative to other galaxies. The classification and comparison of motions (called kinematics) is often challenging. 2-2 Position and Displacement To locate an object means to find its position relative to some reference point, often the origin (or zero point) of an axis such as the x axis in Fig. 2.1. The positive direction of the axis is in the direction of increasing numbers (coordinates), which is toward the right in Fig. 2.1. The opposite direction is the negative direction. For example, a particle might be located at x = 5 m, which means that it is 5 m in the positive direction from the origin. If it were at x = -5 m, it would be just as far from the origin but in the opposite direction. A plus sign for a coordinate need not be shown, but a minus sign must always be shown. A change from one position x1to another position x2is called a displacement x, where ....2.1 When numbers are inserted for the position values x1and x2, a displacement in the positive direction (toward the right in Fig. 2-1) always comes out positive, and one in the opposite direction (left in the figure), negative. For example, if the particle moves from x1= 5 m to x2
Chapter Three Motion in One Dimension Dr. Mukhlis M. Ismail2= 12 m, then x = (12 m) - (5 m) = +7 m. A plus sign for a displacement need not be shown, but a minus sign must always be shown.
Chapter Three Motion in One Dimension Dr. Mukhlis M. Ismail32.2 2-3 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). As a simple example, Fig. 2.2 shows the position function x(t) for a stationary armadillo (which we treat as a particle) at x= -2 m. Figure 2.3a, also for an armadillo, is more interesting, because it involves motion. The armadillo is apparently first noticed at t = 0 when it is at the position x = -5 m. It moves toward x = 0, passes through that point at t = 3 s, and then moves on to increasingly larger positive values of x.Figure 2-3b depicts the actual straight-line motion of the armadillo and is something like what you would see. The graph in Fig. 2-3a is more abstract and quite unlike what you would see, but it is richer in information. It also reveals how fast the armadillo moves. The x-component of average velocity, or average x-velocity, is the x-component of displacement, x, divided by the time interval t during which the displacement occurs. We use the symbol vav-xfor average x-velocity As an example, for the dragster x1= 19 m. x2= 277 m. t1= 1.0 s, and t2= 4.0 s, so As an example, for the dragster x1= 277 m. x2= 19 m. t1= 16.0 s, and t2= 25.0 s, so A common unit for av-xis the meter per second (m/s).
Chapter Three Motion in One Dimension Dr. Mukhlis M. Ismail4total distance A t ... 2.3 sava= Fig. 2.3
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