For one-dimensional motion, we said the average velocity for a time interval equals the displacement divided by the size of the time interval. It is a positive or negative number -- a scalar. For motion in 2 and 3 dimensions, the average velocity is also the displacement divided by the time interval. But since the displacement is now a vector, the average velocity is a vector too! In fact, dividing a vector (e.g., displacement) by a scalar (the time interval) always produces a vector -- one that's in the same direction as the original vector, but with its magnitude divided by the scalar. For instance, if the displacement is 3 m in the NW direction over a time interval of 6 s, then the average velocity will be a 0.5 m/s in the NW direction.
Instantaneous velocity is just the average velocity taken over a time interval that becomes shorter and shorter (approaching zero), just like in one-dimensional motion. In 2- and 3-d motion, of course, the instantaneous velocity remains a vector. The direction of the vector is the direction of the motion at that instant, and its magnitude is called the instantaneous speed.
Calculate the velocity of each displacement vector. The time interval of each interval is 10 minutes. Record your data on the worksheet under column 4, 5, and 6.
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© April, 1998, Montana State University-Bozeman
