# Velocity, Speed, and Motion... Oh My!

Velocity and speed are very similar ideas, but velocity is a vector, and speed is not. Suppose we knew that someone was driving at thirty-five kilometers an hour (35 km/hr), but the direction wasn't given. How would you draw an arrow to represent a vector? You can't know how to draw the vector if you only have one value (either amount or direction). In this example, you were never told about the direction. Physicists would say that the speed is thirty-five kilometers an hour (35 km/hr), but the velocity is unknown. On the other hand, if you're moving at 35 km/hr in a northern direction, then you would have an arrow pointing north with a length of 35. Physicists would say that the velocity is 35 km/hr north.

Velocity is the rate of motion in a specific direction. I'm going that-a-way at 30 kilometers per hour. My velocity is 30 kilometers per hour that-a-way. Average speed is described as a measure of distance divided by time. Velocity can be constant, or it can change (acceleration). Speed with a direction is velocity.

Remember vectors? You will use a lot of vectors when you work with velocity. Our real world example of navigation on the ocean used velocity for every vector. Velocity is a vector measurement because it has an amount and a direction. Speed is only an amount (a scalar). Speed doesn't tell the whole story to a physicist. Think of it another way. If I tell you I'm driving north and ask you how long until we get to the city. You can't know the answer since you don't know my speed. You need both values.

# One Moment in Time

There is a special thing called instantaneous velocity. That's the velocity at a split second in time. Above, we were talking about your speed and direction over a long period of time. Why would you need to measure a velocity at one moment? Think about the moment you drove over the manhole. It's important to know if you were going 1 km/hr when you drove over the manhole, or 60 km/hr. It wouldn't help you to know that your average speed was 30 km/hr.

The term "instantaneous" refers to something physicists call a limit. Scientists "limit" the amount of time they do the measurement. When the "limit" moves to zero, that limit is one tiny moment in time. A physicist would measure your velocity as the "limit for a period of time", zero, to get the instantaneous velocity.