Physics I For Dummies. Steven Holzner

      The direction of the average velocity is just the direction between the start and end points. But if you’re interested in your average speed along either of the two legs of the trip, you have to measure the time it takes for a leg and divide the length of that leg by that time to get the average speed.

      To calculate the average speed over the whole trip, you look at the whole distance traveled, which is , not just 85 miles. And 110 miles divided by 2.0 hours is 55 miles per hour; this is your average speed.

      As another illustration of the difference between average speed and average velocity, consider the motion of the Earth around the sun. The Earth travels in its nearly circular orbit around the sun at an enormous average speed of something like 18 miles per second! However, if you consider one full revolution of the Earth, the Earth returns to its original position, relative to the sun, after one year. After one year, there’s no displacement relative to the sun, so the Earth’s average velocity over a year is zero, even though its average speed is enormous!

Speeding Up (Or Down): Acceleration

      Acceleration is a measure of how quickly your velocity changes. When you pass a parking lot’s exit and hear squealing tires, you know what’s coming next — someone is accelerating to cut you off. After he passes, he slows down right in front of you, forcing you to hit your brakes to slow down yourself. Good thing you know all about physics.

      Like speed, acceleration takes many forms that affect your calculations in various physics situations. In different physics problems, you have to take into account the direction of the acceleration (whether the acceleration is positive or negative in a particular direction), whether it’s average or instantaneous, and whether it’s uniform or nonuniform. This section tells you more about acceleration and explores its various forms.

      Defining acceleration

      Given the initial and final velocities, v_i and v_f, and the initial and final times over which your speed changes, t_i and t_f, you can also write the equation like this:

      Acceleration, like velocity, is actually a vector and is often written as a, in vector style (see Chapter 4). In other words, acceleration, like velocity but unlike speed, has a direction associated with it.

      Determining the units of acceleration

      You can calculate the units of acceleration easily enough by dividing velocity by time to get acceleration:

In terms of units, the equation looks like this:

      Distance per time squared? Don’t let that throw you. You end up with time squared in the denominator because you divide velocity by time. In other words, acceleration is the rate at which your velocity changes, because rates have time in the denominator. For acceleration, you see units of meters per second², centimeters per second², miles per second², feet per second², or even kilometers per hour².

      

It may be easier, for a given problem, to use units such as mph/s (miles per hour per second). This would be useful if the velocity in question had a magnitude of something like several miles per hour that changed typically over a number of seconds.

      Looking at positive and negative acceleration

      Just as for displacement and velocity, acceleration can be positive or negative. This section explains how positive and negative acceleration relate to changes in speed and direction.

      Changing speed

      The sign of the acceleration tells you whether you’re speeding up or slowing down (depending on which direction you’re traveling).

      For example, say that you’re driving at 75 miles per hour, and you see those flashing red lights in the rearview mirror. You pull over, taking 20 seconds to come to a stop. The officer appears by your window and says, “You were going 75 miles per hour in a 30-mile-per-hour zone.” What can you say in reply?

      You can calculate your rate of acceleration as you pulled over, which, no doubt, would impress the officer — look at you and your law-abiding tendencies! You whip out your calculator and begin entering your data. Remember that the acceleration is given in terms of the change in velocity divided by the change in time:

Plugging in the numbers, your calculations look like this:

      Your acceleration was 3.8 mph/s. But that can’t be right! You may already see the problem here; take a look at the original definition

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