Let v (t) be the velocity of a particle moving in the plane.Let s(t) be the magnitude of
Chapter 17, Problem 51(choose chapter or problem)
Let v (t) be the velocity of a particle moving in the plane.Let s(t) be the magnitude of v and let (t) be the angleof v (t) with the positive x-axis at time t, so thatv = s cos i + s sin j .Let T be the unit vector in the direction of v , andlet N be the unit vector in the direction of k v , perpendicularto v . Show that the acceleration a (t) is givenbya = dsdt T + sddt N . This shows how to separate the acceleration into the sumof one component, dsdt T , due to changing speed and aperpendicular component, sddt N , due to changing directionof the motion.
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