A particle moves so that its position vector is given byr=cost i +sint j where i

Question

A particle moves so that its position vector is given byr=cost i +sint j where is constant show that a)the velocity of particle V is perpedicular tor(position vector) b)the acceleration is directed towords the origion and itsmagnitude propotional to the distance from the origion A particle moves so that its position vector is given byr=cost i +sint j where is constant show that a)the velocity of particle V is perpedicular tor(position vector) b)the acceleration is directed towords the origion and itsmagnitude propotional to the distance from the origion

Explanation / Answer

a) velocity is derivative of r so v= dr/dt = -w*sinwt i +w*coswt j to show they are perpendicular check their dot (scalar)products. if scalar pr. of 2 vectors is zero then they areperpendicular: v*r = w*sinwt*coswt +w*coswt*sinwt = 0 YES they are perpendicular b) a= dv/dt= -w^2 * coswt i -w^2*sinwt j = (-w^2)* r (t) snce w is a number so acceleration is directed -r so it istowards origin. magnitude is since a(t) = w^2*r(t) magnitud |a| = w^2 *|r| so it is proportional to the magnitude of r which is thedistance from origin

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