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Problem Zero: Read the section and make your own summary of the material.

Short Answer

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MOTION:

1.DisplacementVersusDistanceTravelled:Letthevector-valuedfunctionr(t)representthepositionfunctionforaparticletravellingonacurveC.IfthedomainofrisanintervalIcontainingpointsaandb:(a)Thedisplacementofthetheparticlefromatobisgivenbythevectorr(b)r(a).(b)Thedistancetravelledbytheparticlefromatobisgivenbythescalarabr'(t)dt.

2.TheTangentialandNormalComponentsofAcceleration:Letr(t)beatwice-differentiablevectorfunctionwitheithertwoorthreecomponentsandwithderivativesr'(t)=v(t)andr''(t)=a(t).ThenthetangentialcomponentofaccelerationaTisgivenbyaT=v.avandthenormalcomponentofaccelerationaNisgivenbyaN=vav.

Step by step solution

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Given is the text on the topic Motion.

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Step 2. Summary of the text given.

MOTION:

1.DisplacementVersusDistanceTravelled:Letthevector-valuedfunctionr(t)representthepositionfunctionforaparticletravellingonacurveC.IfthedomainofrisanintervalIcontainingpointsaandb:(a)Thedisplacementofthetheparticlefromatobisgivenbythevectorr(b)r(a).(b)Thedistancetravelledbytheparticlefromatobisgivenbythescalarabr'(t)dt.

2.TheTangentialandNormalComponentsofAcceleration:Letr(t)beatwice-differentiablevectorfunctionwitheithertwoorthreecomponentsandwithderivativesr'(t)=v(t)andr''(t)=a(t).ThenthetangentialcomponentofaccelerationaTisgivenbyaT=v.avandthenormalcomponentofaccelerationaNisgivenbyaN=vav.

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