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.
The instantaneous velocity v of a particle is always tangent to the path of the particle. 3.1.3 Acceleration If a particle’s velocity changes by ∆v in a time period ∆t, the average acceleration a for that period is a = ∆v ∆t = ∆vx ∆t i+ ∆vy ∆t j+ ∆vz ∆t k (3.10)
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