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High School Precalculus: Help and Review32 chapters | 297 lessons

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Lesson Transcript

Instructor:
*Yuanxin (Amy) Yang Alcocer*

Amy has a master's degree in secondary education and has taught math at a public charter high school.

Velocity in math is similar to speed, with only one difference. Learn what that difference is, how to write velocity, and how to calculate velocity problems.

**Velocity** is defined as the rate of travel of an object, along with its direction. Velocity tells you how fast an object is moving as well as in what direction it is moving. It is similar to speed, except that it also adds direction. So, while speed is directionless, velocity is directional speed.

Speed only gives you a number that tells you how fast you are going. Velocity, because it adds direction, tells you how fast you are changing your position. Because of this difference, if your position doesn't change even if you are moving very fast, your velocity will be zero. If you were to run in place very fast, your speed may be six mph, but your velocity would be zero because you aren't going anywhere. If you were to run backwards and forwards, always returning to your same spot, your velocity would be zero again because you didn't go anywhere.

So remember that for velocity, your position needs to change, but for speed it doesn't. You can go as fast as you can in the same spot without gaining any velocity. But if you are moving forward in a particular direction, then you would be gaining velocity. For velocity, you need to be moving somewhere; you can't be stationary.

The equation or formula for velocity is similar to speed.

To figure out velocity, you divide the distance by the time it takes to travel that same distance, then you add your direction to it. For example, if you traveled 50 miles in 1 hour going west, then your velocity would be 50 miles/1 hour westwards, or 50 mph westwards.

Calculating velocity is a lot like calculating speed, with the addition of taking into account the direction in which you are moving. In order to figure out velocity, your problem would have to allow you to calculate the speed along with what direction the object is moving in. Without the directional information, you can't calculate velocity.

Let's try a problem to see how it works. Let's say that Aunt Martha wants to drive to visit her nephews and nieces. She lives 500 miles away from them, to the north. She has allotted nine hours for travel time. What velocity must she maintain in order to make it there in nine hours? To answer this question, we need to think a little. We have a formula we can use, so we can plug our information in.

If we divide 500 by 9, we get 55.56 mph. We don't have a direction yet, so that is still a speed. To turn that into a velocity, we need a direction. But what direction does Aunt Martha need to drive to reach her nieces and nephews? The problem says she lives 500 miles to the north, so she would need to go the other way, which is south. So that means our velocity is 55.56 mph southwards.

Let's review. **Velocity** is speed with direction. Even if you were going very fast, your velocity may very well be zero if you haven't gone anywhere, like if you were running in place. But if you are moving forwards in a direction, then your velocity is your speed with the direction you are moving in. To calculate velocity, you divide your distance traveled by the time it took to travel that distance and you add your direction to it.

Speed is how fast you're going. **Velocity** adds direction to speed; it is the rate of travel in a particular direction. To calculate velocity, divide distance traveled by the time it took to travel that distance and add direction. If one's position does not change, velocity is zero.

Upon reading about velocity in this lesson, you should be able to

- Define velocity.
- Explain the difference between velocity and speed.
- Calculate for velocity.

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High School Precalculus: Help and Review32 chapters | 297 lessons

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