Solution to problem 7.7.15 from the collection of Kepe O.E.

7.7.15 The equation for the motion of a point along a trajectory is given: s = 0.1 t² + 0.2 t. Determine its normal acceleration at time t = 6 s. In the position occupied by the point at this moment, the radius of curvature of the trajectory is ? = 0.6 m. (Answer 3.27)

The equation for the motion of a point along the trajectory s = 0.1t is given² + 0.2t. The normal acceleration of a point at time t = 6 s can be determined using the formula a_n = v²/? , where v is the speed of the point at time t. Let's differentiate the equation of motion with respect to time to find the speed: v = ds/dt = 0.2 + 0.2t. We substitute t = 6 s and get v = 1.4 m/s. The radius of curvature of the trajectory can be found using the formula: = |(1 + (ds/dt)²)^3/2 / d²s/dt²|, where d²s/dt² - radial acceleration. Let's differentiate the equation of motion again to find the radial acceleration: d²s/dt² = 0.2 m/s². Substitute into the formula for the radius of curvature? = 0.6 m and we get the answer: 3.27.

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This digital product is a solution to problem 7.7.15 from the collection of Kepe O.?. in physics, which consists in determining the normal acceleration of a point along a given trajectory at time t = 6 s. Also in the problem the radius of curvature of the trajectory at this moment in time is known.

The solution to the problem is presented in electronic form and is available for download immediately after purchase in the digital goods store. This is a convenient and quick way to get a ready-made solution to a problem without having to waste time solving it yourself.

The solution to the problem was carried out by an experienced specialist in accordance with the requirements of the textbook. It contains a detailed description of the solution steps, formulas and calculations necessary to obtain the result.

In addition, the solution is made in a beautiful html design, which makes it attractive and easy to read. By purchasing this digital product, you receive a guaranteed solution to the problem that will help you better understand the material and prepare for exams or tests.

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Solution to problem 7.7.15 from the collection of Kepe O.?. consists in determining the normal acceleration of a point along a trajectory and the radius of curvature of the trajectory at time t = 6 s.

To do this, it is necessary to calculate the first and second derivatives of the equation of motion of a point along a trajectory. The first derivative determines the speed of the point, and the second derivative determines the acceleration of the point.

The normal acceleration of a point in this problem is defined as the ratio of the square of the velocity to the radius of curvature of the trajectory at a given point.

Substituting the known values, we find that the normal acceleration at time t = 6 s is 3.27 m/s².

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