Solution to problem 13.2.18 from the collection of Kepe O.E.

13.2.18 It is necessary to calculate the path that a material point of mass m will travel along the Ox axis in time t=1s if it moves under the influence of force Fx=12mt2. It is known that at time t0=0 the coordinate is x0=3 m, and the speed is vх0=6 m/s. (Answer 10).

To solve this problem, it is necessary to use the equation of motion of a material point: x = x0 + v0t + (at^2)/2, where x0 is the initial coordinate, v0 is the initial velocity, a is the acceleration.

Substituting the known values, we get: x = 3 + 6t + (12m/2)t^2. Since we need to find a path, we need to integrate the resulting equation over time from 0 to 1 second:

∫(0→1) x dt = ∫(0→1) (3 + 6t + (12m/2)t^2) dt = 3t + 3t^2 + (12m/6)t^3 |(0→1) = 3 + 3 + 4m = 6 + 4m.

Thus, the material point will travel along the Ox axis a path equal to 6 + 4m meters. By substituting the time value t=1s and equating the equation of motion to zero, we can find the value of mass m, which is equal to 10 kg.

Solution to problem 13.2.18 from the collection of Kepe O.?.

Our product is a solution to one of the problems from the collection of Kepe O.?. in physics. Problem 13.2.18 requires calculating the path traveled by a material point of mass m along the Ox axis in time t=1s, moving under the influence of force Fx=12mt2.

Our team of physics experts provides a detailed solution to this problem with beautiful html design. We use the equations of motion of a material point to calculate the path it will travel in a specified time.

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Our product is a solution to problem 13.2.18 from the collection of Kepe O.?. in physics. This task requires calculating the path traveled by a material point of mass m along the Ox axis in time t=1s, moving under the influence of force Fx=12mt2. We provide a detailed solution to this problem, using the equations of motion of a material point to calculate the path it will travel in a given time.

Our product is a digital good that can be purchased and downloaded from our website to any device. We guarantee the quality of our solution and the accuracy of the answer, which is 10 meters with a mass of a material point equal to 10 kg.

By purchasing this product, you not only get a solution to the problem, but also the opportunity to better understand the laws of physics and apply them to solve similar problems in the future.

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Solution to problem 13.2.18 from the collection of Kepe O.?. consists in determining the path that a material point of mass m will travel along the Ox axis in time t = 1 s, provided that it is acted upon by a force Fx = 12 mt2.

To solve the problem it is necessary to use the equations of motion of a material point. According to Newton's law, the sum of all forces acting on a material point is equal to the product of the mass and the acceleration of this point. In this case, force Fx = 12 mt2, and acceleration a = Fx/m = 12t2.

Using the equations of motion, you can find the x coordinate of a material point at time t:

x = x0 + vxt + (at2)/2

where x0 is the initial coordinate, vх is the initial velocity, t is time, a is acceleration.

Substituting the known values, we get:

x = 3 + 6t + (12t2)/2 = 3 + 6t + 6t2

Now, to determine the path traveled by a material point in time t = 1 s, it is necessary to substitute the time value into the resulting formula:

x = 3 + 61 + 61^2 = 3 + 6 + 6 = 15 (m)

Answer: 15 m.

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