Solution to problem 14.3.3 from the collection of Kepe O.E.

Problem 14.3.3 states: an object with a mass of 2 kg is acted upon by a force whose value varies in accordance with the law F = 6t2. It is required to find the speed of this object at time t = 2 s, if the initial speed v0 is 2 m/s. The answer to the problem is 10 m/s.

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We present to your attention a digital product - a solution to problem 14.3.3 from the collection of Kepe O.?. This task is to determine the speed of a material point weighing 2 kg at time t = 2 s, if it is acted upon by a force whose value varies according to the law F = 6t2, and the initial speed is 2 m/s.

In our digital product you will find a complete description of the problem conditions and its analysis, as well as a step-by-step solution. We provide you with a quick and easy experience using our beautiful HTML design.

Our digital product is an indispensable assistant in teaching physics and mathematics, as well as in preparing for exams and testing. You can easily purchase it from our digital store and start using it right away! The answer to Problem 14.3.3 is 10 m/s.

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Solution to problem 14.3.3 from the collection of Kepe O.?. consists in determining the speed of a material point weighing 2 kg at time t = 2 s, with a given initial speed v0 = 2 m/s and the force acting on the point.

To solve the problem, it is necessary to use Newton's law: F = ma, where F is the force acting on a material point, m is its mass, and is the acceleration of the point.

To determine the acceleration of a point, it is necessary to use the law of change in momentum: Fdt = m(dv), where dt is the time during which the force F acts, dv is the change in the speed of the material point during this time.

Integrating this equation from the initial time t = 0 to the time t = 2 s, we obtain: ∫Fdt = ∫m(dv), where integration is performed from 0 to 2 s.

Substituting the value of force F = 6t2 and mass m = 2 kg, we obtain: ∫0^2 6t^2 dt = ∫v0^v dv.

Having calculated the integrals, we obtain: v - v0 = 2 m/s * 2^3 / 3, where v is the desired speed of the material point at time t = 2 s.

Thus, by solving this problem, you can get the answer: the speed of a material point at time t = 2 s is equal to 10 m/s.

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