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Vector addition

Every force in our particle system can be represented with a vector, which describes size and direction. Vectors are drawn as arrows, with the tail and head showing direction and the length indicating magnitude. To add two vectors, we use the head-to-tail rule. Place the tail of the second vector at the head of the first vector. Then, draw a new vector from the tail of the first vector to the head of the second vector. This new vector is the sum!

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Video transcript

- You should now have a good feeling for the relationship between position, speed and acceleration. Before we can (mumbles) formulas to describe how the particles will move based on the laws of physics, We need to revisit how we think about the speed of the particle. We need to know not only how fast it's moving, but also the direction of motion. In this case downward. We are using idea called a vector to represent things that have both the size and the direction. Vectors are joined as arrows. The direction is which way it's pointing, and the length of the arrow called the magnitude of the vector, indicates it's size. We call this point, the tail of the vector, and this point, the head of the vector. A vector called the velocity, is used to describe the speed and direction of the particle. A short vector means the particle is moving slowly. A long vector indicates that the particle is moving quickly. In this diagram the balls motion is downward, so the velocity vector points downward. If the particle is accelerating, for instance due to gravity, the length of the velocity vector will increase over time since the speed is increasing. Acceleration is also a vector because it too, has a magnitude in direction. But notice the size of the acceleration vector doesn't change as the ball falls. As we saw on the last video, a particle falling under the influence of gravity has a constant acceleration. That is both the direction and size of the acceleration vector is constant. As shown here. We also need to add vectors together. We do this using the head to tail rule. For example, if we need to add vectors v and w, we move w so that v's head is at w's tail. Like this. The resulting vector written v+w, goes from v's tail to w's head. Okay, that's a lot of new ideas. So let's pass here for you to use the next exercise to try this all out. We couldn't make our films without vectors. Vectors are being used any time you see anything moving in our films.