In physics, velocity, which is the rate of change of position (or speed in a particular direction), is a vector. Imagine that you just hit a ground ball on the baseball diamond and you’re running along the first-base line, or the s vector, 90 feet at a 45-degree angle to the positive x-axis. But as you run, it occurs to you to ask, “Will my velocity enable me to evade the first baseman?” A good question, because the ball is on its way from the shortstop.
Whipping out your calculator, you figure that you need 3.0 seconds to reach first base from home plate; so what’s your velocity? To find your velocity, you quickly divide the s vector by the time it takes to reach first base:
This expression represents a displacement vector divided by a time, and time is just a scalar. The result must be a vector, too. And it is: velocity, or v:
Your velocity is 30 feet/second at 45 degrees, and it’s a vector, v.
Dividing a vector by a scalar gives you a vector with potentially different units and the same direction.
In this case, you see that dividing a displacement vector, s, by a time gives you a velocity vector, v. It has the same magnitude as when you divided a distance by a time, but now you see a direction associated with it as well, because the displacement, s, is a vector.