Doing it twice (the derivative of a derivative) gives you a second derivative. Doing it once gives you a first derivative. The derivative is a mathematical operation that can be applied multiple times to a pair of changing quantities. a =Īcceleration is the derivative of velocity with time, but velocity is itself the derivative of position with time. Instantaneous acceleration is then the limit of average acceleration as the time interval approaches zero - or alternatively, acceleration is the derivative of velocity. The limit of a rate as the denominator approaches zero is called a derivative. It's a mathematical ideal that can only be realized as a limit. The word short in this context means infinitely small or infinitesimal - having no duration or extent whatsoever. In contrast, instantaneous acceleration is measured over a "short" time interval. Average acceleration is a quantity calculated from two velocity measurements. The velocity at the beginning of this interval is called the initial velocity, represented by the symbol v 0 (vee nought), and the velocity at the end is called the final velocity, represented by the symbol v (vee). The word long in this context means finite - something with a beginning and an end. Average acceleration is determined over a "long" time interval. Much like velocity, there are two kinds of acceleration: average and instantaneous. Acceleration occurs anytime an object's speed increases or decreases, or it changes direction. Thus, a falling apple accelerates, a car stopping at a traffic light accelerates, and the moon in orbit around the Earth accelerates. That's because acceleration depends on the change in velocity and velocity is a vector quantity - one with both magnitude and direction. Yes, that's right, a change in the direction of motion results in an acceleration even if the moving object neither sped up nor slowed down. This example illustrates acceleration as it is commonly understood, but acceleration in physics is much more than just increasing speed.Īny change in the velocity of an object results in an acceleration: increasing speed (what people usually mean when they say acceleration), decreasing speed (also called deceleration or retardation), or changing direction (called centripetal acceleration). When a commercial shouts "zero to sixty in six point seven seconds" what they're saying here is that this particular car takes 6.7 s to reach a speed of 60 mph starting from a complete stop. For many Americans, their only experience with acceleration comes from car ads. In everyday English, the word acceleration is often used to describe a state of increasing speed. Acceleration is the rate of change of velocity with time. So the changes in your weight shown on the scale actually are a measure of changes in your acceleration.When the velocity of an object changes it is said to be accelerating. Your speed and direction are changing, as the elevator moves faster or slower and goes up or down. Actually, it's your acceleration that is changing. Exactly what is changing as you move upward and downward in the elevator? It isn't your mass-the amount of matter in your body. When it accelerates upward and you feel heavier, the readout increases when it accelerates downward and you feel lighter, the readout decreases. Stand on a bathroom scale in the elevator, and you'll see that the effect is real: the readout on the scale does indeed change as the elevator accelerates. Did You Know? Most people know that an object has weight because of the pull of gravity, but did you know that weight is actually an indication that an object is being accelerated? When you're in an elevator, for example, as the elevator accelerates upward or downward you feel as if your weight is changing-you feel heavier when the elevator is accelerating upward, and lighter as it accelerates downward.
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