Solution to problem 7.6.1 from the collection of Kepe O.E.

7.6.1 A point moves in a circle according to the equation s = t³ + 2t² + 3t. Determine the curvilinear coordinate of a point at the moment of time when its tangential acceleration is a? - 16 m/s². (Answer 22)

There is a point that moves in a circle. Its motion is described by the equation s = t³ + 2t² + 3t, ​​where s is the curvilinear coordinate of the point, and t is time. It is necessary to determine the value of s at the moment of time when the tangential acceleration of the point is -16 m/s². Answer: 22.

Solution to problem 7.6.1 from the collection of Kepe O.?.

This solution is a digital product that is available for purchase in a digital goods store. It is intended for students and teachers taking a mathematics course.

Solution to problem 7.6.1 from the collection of Kepe O.?. contains a detailed description of the solution to this problem, based on the knowledge and principles of mathematics. Beautiful design in HTML format will make the use of this material as convenient and effective as possible.

By purchasing this digital product, you will gain access to high-quality material that will help you gain a deeper understanding of math concepts and solve problems successfully.

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Solution to problem 7.6.1 from the collection of Kepe O.?. is a digital product designed for students and teachers taking a mathematics course. This problem considers the motion of a point in a circle, described by the equation s = t3 + 2t2 + 3t, ​​where s is the curvilinear coordinate of the point, and t is time. It is required to determine the value of the curvilinear coordinate s at the moment of time when the tangential acceleration of the point is equal to -16 m/s2.

The solution to the problem is based on the knowledge and principles of mathematics. The solution contains detailed calculations that allow you to obtain an answer to the problem. The solution is designed in HTML format, which makes its use as convenient and efficient as possible.

By purchasing this digital product, you will gain access to high-quality material that will help you gain a deeper understanding of math concepts and solve problems successfully. Solution to problem 7.6.1 from the collection of Kepe O.?. is a quality product for effective teaching of mathematics. The answer to the problem is 22.

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Problem 7.6.1 from the collection of Kepe O.?. consists in determining the curvilinear coordinate of a point moving in a circle at the moment of time when its tangential acceleration is equal to -16 m/s².

To solve the problem, it is necessary to use the formula for the tangential acceleration of a point moving in a circle: a = Rω², where R is the radius of the circle, and ω is the angular velocity of the point.

From the equation of motion of a point s = t³ + 2t² + 3t, ​​one can determine the speed and angular velocity of the point: v = ds/dt = 3t² + 4t + 3, ω = v/R.

Substituting the expression for ω into the formula for tangential acceleration, we obtain: a = (3t² + 4t + 3)²/R.

It is known that at the moment of time when a = -16 m/s², it is necessary to find the value of the curvilinear coordinate s.

Having solved the equation for a, we find the value of time t = -1. Substituting it into the equation for s, we get s = 22.

Thus, the answer to problem 7.6.1 from the collection of Kepe O.?. equals 22.

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