Читать книгу Physics I For Dummies - Steven Holzner - Страница 67

You relate acceleration, displacement, and time by messing around with the equations until you get what you want. First, note that displacement equals average velocity multiplied by time:

You have a starting point. But what’s the average velocity? If your acceleration is constant, your velocity increases in a straight line from 0 to its final value, as Figure 3-4 shows.

FIGURE 3-4: Increasing velocity under constant acceleration.

The average velocity is half the final velocity, and you know this because there’s constant acceleration. Your final velocity is , so your average velocity is half this:

So far, so good. Now you can plug this average velocity into the equation and get

And this becomes

You can also put in rather than just plain t:

Congrats! You’ve worked out one of the most important equations you need to know when you work with physics problems relating acceleration, displacement, time, and velocity.

Notice that when you derived this equation, you had an initial velocity of zero. What if you don’t start off at zero velocity, but you still want to relate acceleration, time, and displacement? What if you’re initially going 100 miles per hour? That initial velocity would certainly add to the final distance you go. Because distance equals speed multiplied by time, the equation looks like this (don’t forget that this assumes the acceleration is constant):

You also see this written simply as the following (where t stands for , the time over which the acceleration happened):