CALCULUS Understanding Its Concepts and Methods

Velocity vector

If the position of an object in the plane at time
*t*
is given by the coordinates
(*x*(*t*),*y*(*t*)),
then the velocity vector is
**v**(*t*) = (*x'*(*t*),*y'*(*t*)).

If the position of an object in space at time
*t*
is given by the coordinates
(*x*(*t*),*y*(*t*),*z*(*t*)),
then the velocity vector is
**v**(*t*) = (*x'*(*t*),*y'*(*t*),*z'*(*t*)).

If the velocity vector is placed so that it starts at the point
(*x*(*t*),*y*(*t*),*z*(*t*)),
then it lies along the tangent line to the parametric curve. The length or
norm of the velocity vector is the speed of
the object.

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Copyright © 2006 Darel Hardy, Fred Richman, Carol Walker, Robert Wisner. All rights reserved. Except upon the express prior permission in writing, from the authors, no part of this work may be reproduced, transcribed, stored electronically, or transmitted in any form by any method.