Targ SM 1989 K1 option 90

a) Point B moves in the xy plane; the trajectory of the point in the figures is shown conditionally. The law of motion of a point is given by the equations x = f1 (t), y = f2 (t), where x and y are expressed in centimeters, t-in seconds. Find the equation of the trajectory of the point; for the time t1 = 1c, determine the speed and acceleration of the point, as well as its tangential and normal acceleration and the radius of curvature at the corresponding point of the trajectory. b) The point moves along an arc of a circle of radius R = 2m according to the law S = f (t), S- in meters, t - in seconds. Determine the speed and acceleration of the point at time t1 = 1c.