Solution K1-70 (Figure K1.7 condition 0 S.M. Targ 1989)

Task K1-70 (Figure K1.7 condition 0 S.M. Targ 1989) contains two tasks - K1a and K1b, which need to be solved.

In problem K1a, point B moves in the xy plane (see Figures K1.0 - K 1.9, 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, and t in seconds. It is necessary to find the equation of the trajectory of the point, and also for the moment of time t1 = 1 s to determine the speed and acceleration of the point, its tangential and normal accelerations and the radius of curvature at the corresponding point of the trajectory. The dependence x = f1(t) is indicated directly in the figures, and the dependence y = f2(t) is given in table K1 (for figures 0-2 in column 2, for figures 3-6 in column 3, for figures 7-9 in column 4). The figure number is selected according to the penultimate digit of the code, and the condition number in table K1 is selected according to the last one.

In problem K1b, a point moves along a circular arc of radius R = 2 m according to the law s = f(t), given in table K1 in column 5 (s - in meters, t - in seconds), where s = AM is the distance of the point from some origin A, measured along the arc of a circle. It is necessary to determine the speed and acceleration of the point at time t1 = 1 s. In the figure, it is necessary to depict the vectors v and a, assuming that the point at this moment is in position M, and the positive direction of reference s is from A to M.

Solution K1-70 (Figure K1.7 condition 0 S.M. Targ 1989) is a set of problems that includes two tasks - K1a and K1b.

Problem K1a is that point B moves in the xy plane according to the given equations of motion x = f1(t), y = f2(t), where x and y are expressed in centimeters, and t in seconds. It is necessary to find the equation of the point's trajectory, the speed and acceleration of the point at time t1 = 1 s, its tangential and normal accelerations and the radius of curvature at the corresponding point of the trajectory. The dependence x = f1(t) is indicated directly in the figures, and the dependence y = f2(t) is given in table K1 (for figures 0-2 in column 2, for figures 3-6 in column 3, for figures 7-9 in column 4).

Problem K1b is that a point moves along an arc of a circle of radius R = 2 m according to the law s = f(t), given in table K1 in column 5 (s - in meters, t - in seconds), where s = AM - the distance of a point from some origin A, measured along an arc of a circle. It is necessary to determine the speed and acceleration of the point at time t1 = 1 s. In the figure, it is necessary to depict the vectors v and a, assuming that the point at this moment is in position M, and the positive direction of reference s is from A to M.

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Solution K1-70 is a set of problems consisting of two problems - K1a and K1b. In problem K1a, it is required to find the equation for the trajectory of point B moving in the xy plane according to a given law of motion, and also to determine the speed, acceleration, tangential and normal accelerations and the radius of curvature at a given point on the trajectory. The dependence x = f1(t) is given directly in the figures, and the dependence y = f2(t) is given in table K1. In problem K1b, it is required to determine the speed and acceleration of a point moving along an arc of a circle of radius R = 2 m according to a given law s = f(t), and also to depict the velocity and acceleration vectors at a given point in the figure.

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