## Displacement, Velocity, and Acceleration

Much of what we have developed for

One-Dimensional Motioncan be immediately extended tovector notationforTwo-Dimensional Motion.

DisplacementThe location of an object is given by the

displacement vectorthat locates an object relative to some origin.

VelocityAs an object changes its position, we will want to describe how

fastit is moving. As with one-dimensional motion, we will define the average velocity as the ratio of the change in its displacement to the change in time to which that corresponds,Notice that the

velocityand thedisplacementarevectors. We are no longer limited to a change in displacement along a straight line.ris a vector.As with one-dimensional motion, we often want to know about the

instantaneousvelocity,the velocity at this moment. That is the average velocity over a smaller and smaller time interval. As before, thisinstantaneous velocityis often called simpley "the velocity".This limit process, of course, means the

velocityis thetime derivativeof thedisplacement.Remember, velocity

vand displacementrare bothvectors.Notice that the

velocity vectoris tangent to a particle'spath.

AccelerationOf course, we will want to ask how fast the

velocityischanging. Just as earlier, this is theacceleration,This is really the

average accelerationand we can go to theinstantaneous accelerationby using ever smaller time intervals

The vector

acceleration ais the time derivative of thevector velocity. As before, we will usually say "the acceleration" when we mean "theinstantaneousacceleration".

Unit VectorsSummaryReturn to ToC, Vectors(c) 2005, Doug Davis; all rights reserved