Steven Holzner - Physics I For Dummies

Now say that you’re at the end of the first mile and want to see how far you’d have to go — at the same acceleration — to get to 200 miles per hour. Once again, you need to relate velocity, acceleration, and displacement, so this equation is your baby:

Here, you want to solve for s , the displacement, and you get this:

Great. Now for some numbers. In this case, , , and , and you don’t know s at this point. To find s , plug your numbers into the equation you found for s to get

So it would take 3.0 additional miles to get you up to 200 mph.

Here’s one more example. Say you’re in your rocket ship, happily speeding along at some 3.25 kilometers per second (about 7,280 miles per hour) when you see a sign: Speed Zone 215 km Ahead — New Speed Limit: 3.0 km/s.

You jam on the brakes (which are a retro rocket in the front of the rocket ship). The retro rocket is capable of accelerating your ship at –10.0 meters/second 2.

It’s a tense moment. Will you get your speed down to below 3.0 kilometers per second in 215 kilometers of acceleration? Find out, using your old friend:

In this case, you want to solve for the final speed, which is

where , , and . Plugging in the data and solving for v f gives you the following:

Whew, you think — 2.50 kilometers per second is well under the speed limit of 3.0 kilometers per second. You’re safe.

You can now consider yourself a motion master.

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