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Unformatted text preview: Chapter 4 Study Guide for Acceleration 4.1 Changes in velocity Skill 4.1 Understand the relationship between velocity and acceleration Motion with a constant velocity is uniform (zero acceleration). Motion with a changing velocity is accelerated. Just as average velocity is the change in position (displacement) divided by the change in time, so average acceleration is defined as the change in velocity divided by the time interval during which this change occurred. If velocity is measured in m s , then the units of acceleration are ( m s ) s , or m s 2 . Acceleration, like velocity, is a vector : it has a magnitude and a direction. It can be positive or negative depending on how you define your reference axis. When the velocity and acceleration vectors point in the same direction, the object speeds up. When they point in opposite directions, the object slows down. It’s possible for an object to have zero acceleration but nonzero velocity (uniform motion.) It’s also possible to have zero velocity but nonzero acceleration (think, for instance, of a ball at the instant you drop it). Note: The term deceleration is confusing. Just say positive or negative acceleration, even if something is slowing down. Skill 4.2 Be able to look at an x- t plot and draw conclusions about speed, velocity, and acceleration A position vs. time graph for uniform motion is a straight line; for accelerated motion it is a curve. In either case the slope of the curve at any point gives the instantaneous velocity at that time. If the accleration is zero, then the slope of the x- t graph (the time derivative) will be constant. If the acceleration is non-zero, the instantaneous velocity will vary with time. The curvature of a position vs. time graph is a measure of the acceleration . An upward curve (like a smile; concave upward) indicates positive acceleration; downward (like a frown; concave downward) indicates negative acceleration. The sharper the curve, the greater the magnitude of the acceleration. 4.2 Falling and gravitation Skill 4.3 Falling and gravitation Objects falling under the influence of gravity are common examples of accelerated motion, although scientists do not know the cause of gravity. Galileo devised a clever thought experiment (see Figure 4.6) to show that all objects must fall at the same rate in the absence of air resistance . Make sure to try the experiment in Checkpoint 4.5 before lecture. (It’s really quick.) 1 4.3 Free Fall Skill 4.4 Understand what it means for an object to be in free fall In the 2005 textbook, the title for this section is missing. It is the part that comes directly after checkpoint 4.5, and starts with a discussion of figure 4.7. An object that is moving under the influence of gravity alone is in free fall . This means nothing else is pushing or pulling on it. (Even a rock lying still on the ground is being pushed on by the earth, so to be in free fall, the object can’t be touching anything.) The acceleration of an object in free fall is the same for every object, and so it takes the same time for every...
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