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Chapter 11: Q. 13 (page 871)

Completethefollowingdefinition:Ifr(t)=x(t),y(t),z(t)isadifferentiablepositionfunction,thenthevelocityvectorv(t)is....

Short Answer

Expert verified

Ifr(t)=x(t),y(t),z(t)isadifferentiablepositionfunction.Then,v(t)=x'(t),y'(t),z'(t)

Step by step solution

01

Step 1. Given information is:

r(t)=x(t),y(t),z(t)beadifferentiablepositionfunction.

02

Step 2. Velocity Vector

Letcbethespacecurvedefinedbyr(t)=x(t),y(t),z(t),whichisadifferentiablevectorvaluedfunction.Thenthevelocityoftheparticlealongcisgivenby:v(t)=r'(t)v(t)=dr(t)dt=dx(t),y(t),z(t)dt=x'(t),y'(t),z'(t)Thus,v(t)=x'(t),y'(t),z'(t)

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