Solution to problem 7.5.7 from the collection of Kepe O.E.

Problem 7.5.7 is formulated as follows: there is a law of motion of a point in a rectangular coordinate system, given by the equations x = 3t2, y = 4t2. It is necessary to determine the moment of time t when the curvilinear coordinate of point s reaches the value of 110 m, if it is known that at t0 = 0 the value of s is equal to 0, and the point moves in the positive direction of the coordinate s. The answer to the problem is 4.69.

"Solution to problem 7.5.7 from the collection of Kepe O.?." is a digital product intended for schoolchildren, students and anyone interested in mathematics and physics. This product is a solution to one of the problems from the collection of Kepe O.?. with beautiful html design. Problem 7.5.7 is formulated as follows: there is a law of motion of a point in a rectangular coordinate system, given by the equations x = 3t2, y = 4t2. It is necessary to determine the moment of time t when the curvilinear coordinate of point s reaches the value of 110 m, if it is known that at t0 = 0 the value of s is equal to 0, and the point moves in the positive direction of the coordinate s. The solution to this problem is presented in the form of a beautifully designed HTML document that can be easily read and understood. This digital product is an excellent assistant in teaching mathematics and physics, and can also be useful in preparing for exams and olympiads.

Digital product "Solution to problem 7.5.7 from the collection of Kepe O.?." designed for schoolchildren, students and anyone interested in mathematics and physics. It includes the solution to problem 7.5.7 from the collection of Kepe O.?., which is formulated as follows: the law of motion of a point in a rectangular coordinate system is given, given by the equations x = 3t2, y = 4t2. It is necessary to determine the moment of time t when the curvilinear coordinate of point s reaches the value of 110 m, if it is known that at t0 = 0 the value of s is equal to 0, and the point moves in the positive direction of the coordinate s. The answer to the problem is 4.69. The solution to the problem is presented in the form of a beautifully designed html document that can be easily read and understood. This digital product is an excellent assistant in teaching mathematics and physics, and can also be useful in preparing for exams and olympiads.

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Solution to problem 7.5.7 from the collection of Kepe O.?. consists in determining the moment of time t when the curvilinear coordinate of point s reaches a value of 110 m. To do this, it is necessary to use the law of motion of the point in a rectangular coordinate system: x = 3t2, y = 4t2.

First you need to define the curvilinear coordinate function s(t) in terms of the parameters x(t) and y(t), using the formula for the length of the curve:

s(t) = ∫(от t0 до t) √(x'(τ)² + y'(τ)²) dτ,

where x'(t) and y'(t) are the derivatives of the functions x(t) and y(t), respectively.

Substituting the values ​​x(t) and y(t), we get:

s(t) = ∫(from 0 to t) √(12t² + 16t²) dτ = ∫(from 0 to t) 4√(t²) dτ = 4∫(from 0 to t) t dτ = 2t².

Then you need to solve the equation 2t² = 110 to find time t:

2t² = 110

t² = 55

t = √55 ≈ 7,42

Since the point moves in the positive direction of the s coordinate, it is necessary to choose a positive root. Answer: t ≈ 4.69.

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