Relating Position

Relating Position - v ( t ) = x' ( t ) , and a ( t ) = x''...

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Relating Position, Velocity, and Acceleration Combining this latest result with (2) above, we discover that, for constant acceleration a , initial velocity v 0 , and initial position x 0 , x ( t ) = at 2 + v 0 t + x 0 This position function represents motion at constant acceleration, and is an example of how we can use knowledge of acceleration and velocity to reconstruct the original position function. Hence the relationship between position, velocity, and acceleration goes both ways: not only can you find velocity and acceleration from the position function x ( t ) , but x ( t ) can be reconstructed if v ( t ) and a ( t ) are known. (Notice that in this particular case, velocity is not constant: v ( t ) = at + v 0 , and so v = v 0 only at t = 0 .) A natural question to ask might be, "Why stop at acceleration? If
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Unformatted text preview: v ( t ) = x' ( t ) , and a ( t ) = x'' ( t ) , why don't we discuss x''' ( t ) and so forth?" It turns out, the third time derivative of position, x''' ( t ) , does have a name: it is called the "jerk" (honestly). The nice thing is, however, that these higher derivatives don't seem to come into play in formulating physical laws. They exist and we can compute them, but when it comes to writing down force laws (such as Newton's Laws ) which deal with the dynamics of physical systems, they get completely left out. This is why we don't care so much about giving them special names and computing them explicitly....
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This note was uploaded on 02/09/2012 for the course PHY PHY2053 taught by Professor Davidjudd during the Fall '10 term at Broward College.

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