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A racing car moves on a circle of constant radius b.If the speed of the car varies with time t according to the equation v=ct where c is a positive constant, show that the angle between the velocity vector and the acceleration vector is 45 degree at time t=(b/c)^1/2



A small ball is fastened to a long rubber band and is twirled around in such a way that the
ball moves with an elliptical path given by the equation
~r(t) = ˆıb cos ωt + ˆj2b sin ωt
where b and ω are constants. Find the speed of the ball as a function of t. In particular,
find v at t = 0 and at t = π/2ω, at which times the ball is, respectively, at its minimum and
maximum distances from the origin


A bee goes out from its hive in a spiral path given in plane polar coordinates by
r = bekt θ = ct
where b, k and c are positive constants. Show that the angle between the velocity vector and
the acceleration vector remains constant as the bee moves outward.