# Introduction to Vectors

“We’ve reached a velocity of 300mph!” It’s a common phrase you hear on TV, in one way or another. You might be surprised to learn that it’s most often stated entirely wrong. You see, the term “Velocity” is a vector quantity, which probably means nothing to you right now. Hopefully, by the end of your reading you should have an understanding of not only what a vector is but also how to use them in simple physics.

Simply put, a vector is a composite of a direction and of quantity. So to write a velocity, you would say: The velocity is 300mph, northwest. Again, because this is important, a vector has a magnitude
and a direction.

Other examples of vector quantities are:

Momentum

Force

Acceleration

Drag

Lift

Thrust

Displacement

Vectors can have an assortment of mathematical operations applied to them. As an example, let’s use acceleration. If you take an acceleration of 20mph forward and add it to an acceleration of 10mph backward, you get:

>20mph + <10mph = > 10mph

So you have a net acceleration of 10mph forward. It’s the same operation as adding and subtracting positive and negative numbers. Now this is all well and good, as long as we have two perfectly opposing values.

But what if you need to calculate the displacement [that is, how far away an object is from its original position] of a car that goes 4 miles north, and then 3 miles west? Well, it’s not as hard as it sounds. We’re going to have to use the Pythagorean Theorem. Yes, that sounds daunting, but it’s pretty simple. I don’t know why they call such simple things in math and physics “theorems,” or “hypotheses,” to make you feel like you need a PH.D to understand them.

All it involves is a simple equation- a^2 +b^2= c^2 [read a squared plus b squared equals c squared]. To input this into our original problem, we’ll write it like this:

[4×4] + [3×3] + [dxd]

Where “d” equals the displacement, or how far the car has traveled from its original spot.

So: 16+9+ 25

Twenty five is five times five. So the total displacement of the car was five miles from its original position. There is much more to find out about vectors, as I’m sure you know. With the help of trigonometry, vectors are essential to finding the solutions to many common problems, such as an airplanes velocity in respect to wind speed. I hope you continue you study into this subject with enthusiasm.
The passage introduces the concept of vectors and provides an example of calculating displacement using the Pythagorean Theorem. It includes a step-by-step calculation to determine the displacement of a car that travels 4 miles north and 3 miles west.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# Introduction to Vectors

“We’ve reached a velocity of 300mph!” It’s a common phrase you hear on TV, in one way or another. You might be surprised to learn that it’s most often stated entirely wrong. You see, the term “Velocity” is a vector quantity, which probably means nothing to you right now. Hopefully, by the end of your reading you should have an understanding of not only what a vector is but also how to use them in simple physics.

Simply put, a vector is a composite of a direction and of quantity. So to write a velocity, you would say: The velocity is 300mph, northwest. Again, because this is important, a vector has a magnitude
and a direction.

Other examples of vector quantities are:

Momentum

Force

Acceleration

Drag

Lift

Thrust

Displacement

Vectors can have an assortment of mathematical operations applied to them. As an example, let’s use acceleration. If you take an acceleration of 20mph forward and add it to an acceleration of 10mph backward, you get:

>20mph + <10mph = > 10mph

So you have a net acceleration of 10mph forward. It’s the same operation as adding and subtracting positive and negative numbers. Now this is all well and good, as long as we have two perfectly opposing values.

But what if you need to calculate the displacement [that is, how far away an object is from its original position] of a car that goes 4 miles north, and then 3 miles west? Well, it’s not as hard as it sounds. We’re going to have to use the Pythagorean Theorem. Yes, that sounds daunting, but it’s pretty simple. I don’t know why they call such simple things in math and physics “theorems,” or “hypotheses,” to make you feel like you need a PH.D to understand them.

All it involves is a simple equation- a^2 +b^2= c^2 [read a squared plus b squared equals c squared]. To input this into our original problem, we’ll write it like this:

[4×4] + [3×3] + [dxd]

Where “d” equals the displacement, or how far the car has traveled from its original spot.

So: 16+9+ 25

Twenty five is five times five. So the total displacement of the car was five miles from its original position. There is much more to find out about vectors, as I’m sure you know. With the help of trigonometry, vectors are essential to finding the solutions to many common problems, such as an airplanes velocity in respect to wind speed. I hope you continue you study into this subject with enthusiasm.
user
The passage introduces the concept of vectors and provides an example of calculating displacement using the Pythagorean Theorem. It includes a step-by-step calculation to determine the displacement of a car that travels 4 miles north and 3 miles west.

TYPE: SINGLE_QUESTION_WITH_ANSWER