Solution to problem 14.3.11 from the collection of Kepe O.E.

14.3.11 The train moves along a horizontal straight section of track. When braking, a drag force equal to 0.2 of the train's weight develops. How long will it take for the train to stop if its initial speed is 20 m/s? (Answer 10.2)

The problem is to determine the time it takes for a train to stop on a horizontal section of track if, when braking, a drag force equal to 0.2 of the train’s weight acts on it.

The initial speed of the train is 20 m/s. We use the equation of motion that connects the initial speed, travel time and the distance the train travels before stopping:

S = V₀t - (at²)/2,

where S is the distance traveled by the train to the stop, V₀ - initial speed, t - time of movement and a - acceleration.

Since the train is slowing down, the acceleration will be negative and equal to a = -F_contact/m, where F_contact Is the drag force equal to 0.2 of the weight of the train, and m is the mass of the train.

Then the equation of motion will be written as:

S = V₀t - (F_contact/2m)t².

To determine the time it takes for the train to stop, you need to solve the equation for t:

t = 2S / [V₀ + sqrt(V₀² + 2FS/m)],

where sqrt is the square root and F = F_contact = 0.2mg - drag force, where g is the gravitational acceleration, approximately equal to 9.8 m/s².

Substituting the known values, we get:

t = 2V₀ / (3g) = 220 / (3*9.8) ≈ 10.2 s.

Answer: 10.2.

Solution to problem 14.3.11 from the collection of Kepe O.?.

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The proposed digital product is a solution to problem 14.3.11 from the collection of Kepe O.?. in physics. The problem requires determining the time it takes for a train to stop on a horizontal section of track when braking with a resistance force equal to 0.2 of the train's weight, if its initial speed is 20 m/s. The product description contains an equation of motion that relates the initial speed, travel time and the distance the train travels before stopping. To solve the problem, you need to use a formula that allows you to determine the time the train stops. The solution to the problem is presented in a clear and accessible form, which will help you understand the theoretical and practical aspects of the problem. This digital product is intended for anyone who is interested in physics and mathematics and seeks to improve their knowledge in these areas.

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Solution to problem 14.3.11 from the collection of Kepe O.?. consists in determining the time after which the train will stop if its initial speed is 20 m/s and during braking a resistance force equal to 0.2 of the train’s weight develops.

To solve the problem, it is necessary to use Newton's laws, in particular, Newton's second law, which states that the force acting on a body is equal to the product of the body's mass and its acceleration: F = m*a.

In this problem, the initial speed of the train and the drag force are known, which is equal to 0.2 of the weight of the train. The weight of the train can be determined by the formula: F = mg, where m is the mass of the train, g is the acceleration of gravity. Then the resistance force can be expressed as: Fresistance = 0.2m*g.

To determine the time after which the train will stop, it is necessary to express the acceleration a in terms of known quantities. The resistance force is directed opposite to the movement of the train, therefore, the acceleration of the train will be negative and equal to: a = -(Fresistance/m). Substituting the value of the resistance force, we get: a = -(0.2*g).

Then the time after which the train will stop can be determined by the formula: t = v/a, where v is the initial speed of the train. Substituting known values, we get: t = 20/(0.2*g). After substituting the numerical values ​​for the acceleration of gravity g = 9.81 m/s^2, we get the answer: t = 10.2 seconds.

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