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you should now have a good feeling for the relationship between position speed and acceleration before we can develop 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 use an idea called a vector to represent things that have both the size and the direction vectors are drawn as arrows the direction is which way it's pointing and the length of the arrow called the magnitude of the vector indicates its 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 vector because it too has a magnitude and direction but notice the size of the acceleration vector doesn't change as the ball falls as we saw in 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 scale like this the resulting vector written V plus W goes from these tail to WS head okay that's a lot of new ideas so let's pause 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 anytime you see anything moving in our films