Finding Distance Using Initial Velocity, Time, and Acceleration

In a physics equation, given initial velocity, time, and acceleration, you can find an object’s displacement. Here’s an example: There you are, the Tour de France hero, ready to give a demonstration of your bicycling skills. There will be a time trial of 8.0 seconds. Your initial speed is 6.0 meters/second, and when the whistle blows, you accelerate at 2.0 m/s2 for the 8.0 seconds allowed. At the end of the time trial, how far will you have traveled?

You could use the relation s = (1/2)at2, except you don’t start off from zero speed — you’re already moving, so you should use the following:

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In this case, a = 2.0 m/s2, t = 8.0 s, and vi = 6.0 m/s, so you get the following:

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You write the answer to two significant digits — 110 meters — because you know the time only to two significant digits. In other words, you ride to victory in about 110 meters in 8.0 seconds. The crowd roars.

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