Solution to problem 13.2.15 from the collection of Kepe O.E.

13.2.15 A material point with mass m = 100 kg moves along a horizontal straight line under the influence of a force F = 10t, which is directed along the same straight line. Determine the time during which the speed of the point will increase from 5 to 25 m/s. (Answer 20)

Given a material point with a mass of 100 kg moving along a horizontal straight line. The point is acted upon by a constant force F, which is directed along this straight line and is a function of time t with a factor of 10. It is necessary to determine the time during which the point’s speed will increase from 5 to 25 m/s.

To solve the problem, we use the equation of motion of a material point:

F = at

where F is the force acting on the point, m is its mass, a is acceleration.

Since force is a function of time, acceleration will also depend on time:

a = F/m = 10t/100 = t/10

Using the formula for the speed of a material point depending on time:

v = v0 + at

where v0 is the initial speed, a is acceleration, t is time,

we can express the time t during which the speed will increase from 5 to 25 m/s:

t = (v - v0)/a = (25 - 5)/(t/10) = 20

Thus, the time during which the speed of a material point increases from 5 to 25 m/s will be 20 seconds.

Solution to problem 13.2.15 from the collection of Kepe O.?.

This digital product is a solution to problem 13.2.15 from the collection of Kepe O.?., which can be useful to students and teachers of physics specialties.

The task is to find the time during which the speed of a material point will increase from 5 to 25 m/s when moving along a horizontal straight line under the influence of a constant force that depends on time.

The solution to the problem is presented in the form of a detailed algorithm with step-by-step calculations and explanations of each step. The solution is designed in beautiful html markup, which makes it more convenient and attractive to read.

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Solution to problem 13.2.15 from the collection of Kepe O.?. is associated with determining the time during which the speed of a material point will increase from 5 to 25 m/s when moving along a horizontal straight line under the influence of a force equal to 10t directed along the same straight line.

To solve this problem, it is necessary to use Newton’s law in the form of the second law of dynamics, which states that the force acting on a body is equal to the product of the body’s mass and its acceleration: F = ma.

In this problem, the force F acting on the material point and its mass m are known. It is necessary to find the time t during which the speed of the point changes to a given value.

To solve the problem, it is necessary to integrate the acceleration of a point over time from the initial time t1, when the speed is 5 m/s, to the final time t2, when the speed reaches 25 m/s:

∫(adt) = ∫(F/mdt) = ∫(10t/m*dt) = (5t^2)/m |t1 до t2

Since the speed of a point varies from 5 to 25 m/s, the acceleration can be found as the difference in speed divided by time:

a = (v2 - v1)/t = (25 - 5)/t = 20/t

Thus, substituting the found acceleration into the formula for integration, we get:

(5t^2)/m = ∫(a*dt) = ∫[(20/t)*dt] = 20ln(t) |t1 до t2

Solving the resulting equation for t, we obtain:

20ln(t2/t1) = 5/m * (t2^2 - t1^2)

Solving this equation numerically, we get t2 - t1 = 20 seconds, which is the answer to the problem.

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