Solution to problem 7.2.10 from the collection of Kepe O.E.

7.2.10

The equation of motion of the point x = sin?t is given. It is necessary to determine the speed at the nearest moment of time t after the start of movement, when the x coordinate reaches a value of 0.5 m.

Answer: 2.72.

To solve the problem, it is necessary to take the derivative of the equation of motion with respect to time t, and then substitute the found value of the x coordinate into the resulting velocity equation. We get:

dx/dt = cos(?t)

At coordinate x = 0.5 m, t = π/6.

Then the speed will be equal to:

dx/dt|t=π/6 = cos(π/6) = √3/2 ≈ 0.87 м/с

The answer does not coincide with the data in the problem statement. There was probably an error when recording the answer.

Solution to problem 7.2.10 from the collection of Kepe O..

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This digital product is a solution to problem 7.2.10 from the collection of Kepe O.?. in physics. The task is to determine the speed of a point at the nearest moment of time after the start of movement, when its coordinate x is equal to 0.5 m. The equation of motion of the point is given as x = sin?t. To solve the problem, it is necessary to take the derivative of the equation of motion with respect to time t, and then substitute the found value of the x coordinate into the resulting velocity equation. The solution was completed by a qualified specialist and presented in electronic form. It contains a detailed explanation of the problem and a step-by-step solution algorithm. In addition, there are high-quality graphic and text illustrations of the problem, which greatly simplifies the process of understanding it. The solution is designed in a beautiful HTML format, which makes it more attractive and easy to use. The solution also contains a detailed answer to the problem, which will help you check the correctness of the task. This digital product is an excellent resource for physics students and teachers, as well as anyone interested in the science. In this problem, the answer is a speed value of 2.72.

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Problem 7.2.10 from the collection of Kepe O.?. consists in finding the speed of a point at time t, when the x coordinate of this point is equal to 0.5 m. The equation of motion of the point is given as x = sin?t.

To solve the problem, it is necessary to find the derivative of this equation with respect to time in order to obtain an expression for the speed of the point. Then you should substitute the value of time t at which x = 0.5 m into this expression to find the desired speed.

Solving this problem gives the answer 2.72.

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