Solution to problem 14.3.2 from the collection of Kepe O.E.

Problem 14.3.2 considers a material point with a mass of 1 kg, which is acted upon by a force of constant direction. The value of this force changes according to the law F = 5 cos ?t. It is necessary to determine the speed of the point at time t = 0.5 s with an initial speed v0 = 1.5 m/s. The solution of the problem is reduced to integrating the equation of motion of a material point. Integrating this equation, we obtain an expression for the speed of a point at time t: v = v0 + (1/m) * ∫(0,t) F(t) dt, where m is the mass of the point. Substituting the values ​​into this expression, we get the answer: v = 3.09 m/s.

Here is the solution to problem 14.3.2 from the collection of Kepe O.?. in the format of a digital product. This product provides a solution to a complex physics problem that can be used by students and teachers in the fields of physics and mathematics. The solution to the problem is presented in the form of a beautifully designed HTML document that is easy to read and understand. It contains a detailed explanation of all solution steps, as well as the formulas and graphs needed to fully understand the problem. This digital product will be useful to anyone interested in physics and mathematics, as well as students and teachers who study these disciplines.

This product is a solution to physical problem 14.3.2 from the collection of Kepe O.?. in digital document format. The task is to determine the speed of a material point weighing 1 kg at time t=0.5 s, which is acted upon by a force of constant direction, the value of which varies according to the law F=5cos(ωt). To solve the problem, it is necessary to integrate the equation of motion of the point and substitute the values ​​into the resulting formula for speed: v = v0 + (1/m) * ∫(0,t) F(t) dt. As a result of the solution, the answer is obtained: the speed of the point at time t=0.5 s is equal to 3.09 m/s. The digital document provides a detailed explanation of all solution steps, formulas and graphics for a better understanding of the problem. This product can be useful to students and teachers in the field of physics and mathematics, as well as anyone interested in these disciplines.

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Problem 14.3.2 from the collection of Kepe O.?. consists in determining the speed of a material point weighing 1 kg at the time t = 0.5 s, if the initial speed of the point is v0 = 1.5 m/s, and it is acted upon by a force of a constant direction, the value of which varies according to the law F = 5 cos? t.

To solve the problem it is necessary to use Newton's laws of dynamics and kinematics formulas.

According to Newton's second law, the force F acting on a material point is equal to the product of the point's mass and its acceleration a: F = ma. Thus, the acceleration of a point is defined as a = F/m.

Using the kinematics formula for uniformly accelerated motion v = v0 + at, we can determine the speed of the point at time t = 0.5 s. Thus, it is necessary to determine the acceleration of a point at time t = 0.5 s, knowing its initial speed and the law of change of force F.

To find the acceleration of a point at time t = 0.5 s, it is necessary to substitute the time value into the law of change of force and solve the resulting equation for acceleration a = F/m. Then, using the found acceleration value and the initial speed of the point, you can find its speed at time t = 0.5 s using the formula v = v0 + at.

So, as a result of solving problem 14.3.2 from the collection of Kepe O.?. the answer is obtained: the speed of a material point weighing 1 kg at the moment of time t = 0.5 s is equal to 3.09 m/s.

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