Transcription of Chapter 3 Motion in Two and Three Dimensions
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Chapter 3 Motion in Two and Three Dimensions
Chapter 3 Motion in Two and Three The Important PositionIn Three Dimensions , the location of a particle is specified by itslocation vector, r:r=xi+yj+zk( )If during a time interval tthe position vector of the particle changes fromr1tor2, thedisplacement rfor that time interval is r=r1 r2( )= (x2 x1)i+ (y2 y1)j+ (z2 z1)k( ) VelocityIf a particle moves through a displacement rin a time interval tthen its average velocityfor that interval isv= r t= x ti+ y tj+ z tk( )As before, a more interesting quantity is theinstantaneousvelocityv, which is the limitof the average velocity when we shrink the time interval tto zero. It is the time derivativeof the position vectorr:v=drdt( )=ddt(xi+yj+zk)( )=dxdti+dydtj+dzdtk( )can be written:v=vxi+vyj+vzk( )5152 Chapter 3.
(a) To clarify matters, what we mean here is that when we use the numerical value of t in seconds, we will get the values of r in meters. Since the velocity vector is the time–derivative of the position vector r, we have: v = dr dt = d dt (i+4t2j+tk) = 0i+8tj +k That is, v = 8tj +k. Here, we mean that when we use the numerical value of t in ...
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