MATH 14 Lecture 2: Math 14 Vector Functions & Motions Sect 13.1 & 13.2 Class Notes
10 Jan 2019
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) properties of the derivatives of vector functions. The position vector function goes from the origin to the location of the particle. ) derivatives of vector functions: since r ( t ) describes position should be velocity. should be acceleration. dr(t) dt mean? r(t+h) r(t) h dr dt d r2 dt2 v ( t ) = a ( t ) = But what does: define dt dr(t) = lim h 0. 3 out of 7 r(t+h) r(t) h. Lim as h 0. is tangent to the particle"s path. dr dt (velocity is tangent to the particle"s path. ) , the unit vector tangent to the path, i simply compute. Note that speed is the instantaneous rate of change of arc length (i. e. path length) with respect to time. 5 out of 7 h h h r(t+h) r(t) f(t+h) f(t)] i h. + g (t)j g(t+h) g(t)] j lim h 0.
