Solution K1-00 (Figure K1.0 condition 0 SM Targ 1988)

Point B moves in the xy plane (Figure K1.0-K1.9, Table K1; 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; for the time instant t1 = 1 s, determine the speed and acceleration of the point, as well as its tangential acceleration and the radius of curvature at the corresponding point of the trajectory. The dependence x = f1 (t) is shown directly in the figures, and the dependence y = f2 (t) is given in Table. K1 (for Figure 0-2 in Column 2, for Figure 3-6 in Column 3, for Figure 7-9 in Column 4).