Solution to problem 13.2.13 from the collection of Kepe O.E.

13.2.13 A material object with a mass of 900 kg moves along a horizontal straight line under the influence of a force F = 270t directed along the same straight line. It is necessary to determine the speed of an object at time t = 10 s if its initial speed at t0 = 0 is v0 = 10 m/s. (Answer 25)

To solve this problem it is necessary to use the equation of motion of a material point:

v = v0 + at,

where v is the speed at time t, v0 is the initial speed (at t0 = 0), a is the acceleration of the material point. The acceleration of a material point can be found using Newton's second law:

F = at,

where F is the force acting on a material point, m is its mass, a is acceleration. Substituting the expression for force F = 270t and mass m = 900 kg, we obtain:

a = F/m = 270t/900 = 0.3t (м/c^2).

Now you can find the speed of a material point at time t = 10 s by substituting the known values ​​into the equation of motion:

v = v0 + at = 10 + 0.3*10 = 13 (м/с).

Thus, the speed of the material point at the moment of time t = 10 s is equal to 13 m/s.

Solution to problem 13.2.13 from the collection of Kepe O..

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We present to your attention a digital product - a solution to problem 13.2.13 from the collection of Kepe O.?. This product will be useful to students and teachers studying physics and mathematics.

The product includes a detailed description of the process of solving the problem, a step-by-step explanation of the formulas and methods used, as well as the answer to the problem. All materials are designed in a convenient and beautiful HTML format.

To solve the problem, it is necessary to use the equation of motion of a material point: v = v0 + at, where v is the speed at time t, v0 is the initial speed (at t0 = 0), a is the acceleration of the material point. The acceleration of a material point can be found using Newton's second law: F = ma, where F is the force acting on the material point, m is its mass, a is acceleration.

Substituting the expression for force F = 270t and mass m = 900 kg, we obtain: a = F/m = 270t/900 = 0.3t (m/s^2). Now you can find the speed of a material point at time t = 10 s by substituting the known values ​​into the equation of motion: v = v0 + at = 10 + 0.3*10 = 13 (m/s).

Thus, the speed of the material point at the moment of time t = 10 s is equal to 13 m/s. By purchasing our digital product, you will receive not only a ready-made solution, but also the opportunity to better understand the material and learn to apply formulas and methods in solving similar problems in the future. Don't miss the opportunity to purchase a healthy, high-quality product at an affordable price!

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Solution to problem 13.2.13 from the collection of Kepe O.?. consists in determining the speed of a material point at the moment of time t = 10 s, moving along a horizontal straight line under the influence of a force F = 270t, which is directed along the same straight line. It is known that the mass of the material point is m = 900 kg, and the initial speed is v0 = 10 m/s at t0 = 0.

To solve the problem, it is necessary to use Newton's laws and kinematic formulas. According to Newton's second law, the force F acting on a material point is equal to the product of the mass of the material point and its acceleration a: F = ma. It is also known that acceleration a is the derivative of speed with respect to time: a = dv/dt.

Therefore, we can write down the equation of motion of a material point: ma = F = 270t. Dividing both sides of the equation by mass, we get the equation for acceleration: a = 270t/m.

Next, it is necessary to find the speed of the material point at the time t = 10 s. To do this, you can use kinematics formulas connecting acceleration, time and speed: v = v0 + at.

Substituting the values ​​from the condition, we get: v = 10 m/s + (270 m/s² * 10 s) / 900 kg * 10 m/s² = 25 m/s.

Thus, the speed of a material point at time t = 10 s is equal to 25 m/s.

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