CALCULUS Understanding Its Concepts and Methods

Acceleration vector

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

The acceleration vector measures the change in the velocity vector—how much the object is speeding up, slowing down, or changing direction. If the acceleration vector is zero, then the object is traveling with a constant velocity. In this animation, the acceleration vector is shown in green. It points in the direction in which the object is being pushed.

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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.