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Unformatted text preview: Chapter 2 Motion in One Dimension 2.1 The Important Stuff 2.1.1 Position, Time and Displacement We begin our study of motion by considering objects which are very small in comparison to the size of their movement through space. When we can deal with an object in this way we refer to it as a particle. In this chapter we deal with the case where a particle moves along a straight line. The particles location is specified by its coordinate, which will be denoted by x or y. As the particle moves, its coordinate changes with the time, t. The change in position from x1 to x2 of the particle is the displacement x, with x = x2 ' x1. 2.1.2 Average Velocity and Average Speed When a particle has a displacement x in a change of time t, its average velocity for that time interval is v = xt = x2 ' x1 t2 ' t1 (2.1) The average speed of the particle is absolute value of the average velocity and is given by s = Distance travelled t (2.2) In general, the value of the average velocity for a moving particle depends on the initial and final times for which we have found the displacements. 2.1.3 Instantaneous Velocity and Speed We can answer the question how fast is a particle moving at a particular time t? by finding the instantaneous velocity. This is the limiting case of the average velocity when the time 27 28 CHAPTER 2. MOTION IN ONE DIMENSION interval t include the time t and is as small as we can imagine: v = lim t!0 xt = dx dt (2.3) The instantaneous speed is the absolute value (magnitude) of the instantaneous velocity. If we make a plot of x vs. t for a moving particle the instantaneous velocity is the slope of the tangent to the curve at any point. 2.1.4 Acceleration When a particles velocity changes, then we way that the particle undergoes an acceleration. If a particles velocity changes from v1 to v2 during the time interval t1 to t2 then we define the average acceleration as v = xt = x2 ' x1 t2 ' t1 (2.4) As with velocity it is usually more important to think about the instantaneous acceleration, given by a = lim t!0 vt = dv dt (2.5) If the acceleration a is positive it means that the velocity is instantaneously increasing; if a is negative, then v is instantaneously decreasing. Oftentimes we will encounter the word deceleration in a problem. This word is used when the sense of the acceleration is opposite that of the instantaneous velocity (the motion). Then the magnitude of acceleration is given, with its direction being understood....
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- Fall '08
- Velocity, Trigraph, Orders of magnitude