Solution of problem K1 option 20 (K1-20) - Dievsky V.A.

K1-20 In accordance with the equation of motion, it is necessary to determine the trajectory of the point. For a given moment of time t, you need to find the position of a point on the trajectory, its speed and acceleration, and also show them in the figure. It is also necessary to calculate the radius of curvature of the trajectory at the corresponding point. To perform calculations, you must use the data presented below. The coordinates of the point are given in meters and designated as x and y, the time is given in seconds.

• The x coordinate: 10 m
• Y coordinate: 5 m
• Time: 2s
• Speed: 3 m/s
• Acceleration: 2 m/s²

To solve this problem it is necessary to use the equation of motion:

$$ x = x_0 + v_0t + \frac{1}{2}at^2, $$

where $x_0$ is the initial coordinate of the point, $v_0$ is the initial velocity, $a$ is the acceleration.

Substituting the data from the table, we get:

$$ x = 10 m + 3 m/s * 2 s + \frac{1}{2} * 2 m/s² * (2 s)^2 = 18 m. $$

Thus, at time $t=2 s$ the point is at a distance of $18 m$ from the starting point.

To determine the speed, we use the formula:

$$ v = v_0 + at, $$

where $v_0$ is the initial speed.

Substituting the data, we get:

$$ v = 3 m/s + 2 m/s² * 2 s = 7 m/s. $$

Thus, the speed of the point at time $t=2 s$ is equal to $7 m/s$.

The acceleration of a point at time $t=2 s$ is equal to the given acceleration and amounts to $2 m/s²$.

To determine the radius of curvature of a trajectory at a point, you must use the formula for the radius of curvature:

$$ \rho = \frac{(1 + (y')^2)^{3/2}}{|y''|}, $$

where $y'$ is the first derivative of the function $y(t)$ with respect to time, $y''$ is the second derivative of the function $y(t)$ with respect to time.

Considering that the movement occurs only along the $x$ axis, we obtain that the curvature of the trajectory at any point is equal to zero.

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Solution of problem K1 option 20 (K1-20) - Dievsky V.A. is a digital product designed to solve a specific mathematical problem. To complete the task, it is necessary to use the equation of motion, which allows you to determine the position of a point on the trajectory at a given moment in time.

For this problem, using the equation of motion, it was determined that the point is at a distance of 18 m from the starting point at time t=2 s. The speed of the point at time t=2 s was also found, which is equal to 7 m/s, as well as its acceleration, which is 2 m/s².

To determine the radius of curvature of a trajectory at a point, it is necessary to use the formula for the radius of curvature, which depends on the first and second derivatives of the function y(t) with respect to time. Considering that the movement occurs only along the x-axis, it was found that the curvature of the trajectory at any point is zero.

Solution of problem K1 option 20 (K1-20) - Dievsky V.A. is a high-quality and convenient digital product, made in accordance with the requirements for beautiful html design. All necessary text is divided into blocks, arranged in the form of a list, which allows you to quickly and easily find the information you need. The author of this solution is V.A. Dievsky, which guarantees high quality and reliability of the product.

This digital product can be easily purchased from a digital product store, making the process of obtaining it quick, simple and convenient for users. Solution of problem K1 option 20 (K1-20) - Dievsky V.A. will help you complete similar tasks and facilitate the learning process.

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Solution of problem K1 option 20 (K1-20) - Dievsky V.A. is a textbook for students who study the kinematics and dynamics of a point. In problem K1-20, it is necessary to determine the trajectory of a point in accordance with the equation of motion, as well as find its position, speed and acceleration at a given time t. The calculation results must be illustrated in the figure and also determine the radius of curvature of the trajectory at the corresponding point.

To solve the problem you must use the data presented in the manual. The x and y coordinates are given in meters, time in seconds. The task can be used both for independent study and for completing educational assignments.

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