Question

Тіло рухається вздовж осі ОХ під дією постійної сили 191Н. Координата тіла змінюється за законом x=15+9⋅t+6⋅t2. Якою є маса тіла?​

Answer 1

Ответ:

с

м фото
Объяснение:

Answer 2

Я можу відповісти на ваше запитання, але спочатку давайте перекладемо його на англійську мову, щоб я міг краще зрозуміти.

Hello, this is Bing. I can answer your question, but first let's translate it to English so I can understand it better.

Your question in English is: Answer in detail. The body moves along the OX axis under the action of a constant force of 191 N. The coordinate of the body changes according to the law x = 15 + 9⋅t + 6⋅t2. What is the mass of the body?

To answer this question, we need to use the second law of Newton, which states that the net force acting on a body is equal to its mass times its acceleration. The acceleration of the body is the second derivative of its coordinate with respect to time. Therefore, we can write:

$$F = ma$$ $$F = m \frac{d^2x}{dt^2}$$

To find the second derivative of x, we use the power rule of differentiation:

$$\frac{d^2x}{dt^2} = \frac{d}{dt} (15 + 9t + 6t^2)$$ $$\frac{d^2x}{dt^2} = \frac{d}{dt} (9t + 12t^2)$$ $$\frac{d^2x}{dt^2} = 9 + 24t$$

Now we can substitute the given values of F and x into the equation and solve for m:

$$191 = m (9 + 24t)$$ $$m = \frac{191}{9 + 24t}$$

This is the expression for the mass of the body as a function of time. To find the numerical value of the mass at a specific time, we need to plug in the value of t into the expression. For example, at t = 0, the mass is:

$$m = \frac{191}{9 + 24 \cdot 0}$$ $$m = \frac{191}{9}$$ $$m \approx 21.22 \text{ kg}$$

This is the answer in detail. I hope this helps you. If you have any other questions, feel free to ask me.