The kinetic energy of a body increases with time according to the law

Let us consider a body weighing 2 kg, the kinetic energy of which increases with time according to the law W = 9t4 J.

To find the path traveled by a body during a period of time from t₁ = 1s to t₂ = 3 s we use the formula:

S = (W₂ - W₁) / F

Where S - the path traveled by the body, W₁ and W₂ - values ​​of the kinetic energy of the body at moments of time t₁ and t₂ respectively, F - a force acting on a body at the same moment in time.

Let's substitute the known values:

S = ((9t⁴₂ - 9t⁴₁) / 2) / F

S = ((9*(3⁴) - 9*(1⁴)) / 2) / F

S = 810 / (2F)

Thus, the path traveled by the body during the time interval from t₁ = 1s to t₂ = 3 s, equals 405 m.

To find the magnitude of the force applied to the body at time t₂, let's use the formula:

F = (W₂ - W₁) / (t₂ - t₁)

Let's substitute the known values:

F = (9t⁴₂ - 9t⁴₁) / (t₂ - t₁)

F = (9*(3⁴) - 9*(1⁴)) / (3 - 1)

F = 486 N

Thus, the magnitude of the force applied to the body at time t₂, equal to 486 N.

Answer: the path traveled by the body during the time interval from t₁ = 1s to t₂ = 3 s, equal to 405 m, the magnitude of the force applied to the body at time t₂, equal to 486 N.

Task 30967.

A detailed solution with a brief record of the conditions, formulas and laws used in the solution, the derivation of the calculation formula and the answer.

If you have any questions about the solution, write, I will try to help.

To solve the problem, it is necessary to find the path traveled by the body during the time interval from t₁ = 1s to t₂ = 3 s, as well as the magnitude of the force applied to the body at time t₂.

The law of change in the kinetic energy of a body is given by the formula: W = 9t⁴ J, body weight m = 2 kg.

To determine the path traveled by a body in a given period of time, we use the formula:

S = (W₂ - W₁) / F, where S - the path traveled by the body, W₁ and W₂ - values ​​of the kinetic energy of the body at moments of time t₁ and t₂ respectively, F - a force acting on a body at the same moment in time.

Let's substitute the known values:

S = ((9t⁴₂ - 9t⁴₁) / 2) / F

Let's calculate the path traveled by the body:

S = ((9*(3⁴) - 9*(1⁴)) / 2) / F = 405 m

Thus, the path traveled by the body during the time interval from t₁ = 1s to t₂ = 3 s, equals 405 m.

To determine the magnitude of the force applied to the body at time t₂, let's use the formula:

F = (W₂ - W₁) / (t₂ - t₁)

Let's substitute the known values:

F = (9t⁴₂ - 9t⁴₁) / (t₂ - t₁)

Let's calculate the magnitude of the force:

F = (9*(3⁴) - 9*(1⁴)) / (3 - 1) = 486 N

Thus, the magnitude of the force applied to the body at time t₂, equal to 486 N.

Answer: the path traveled by the body during the time interval from t₁ = 1s to t₂ = 3 s, equal to 405 m, the magnitude of the force applied to the body at time t₂, equal to 486 N.

Task 30967.

The solution to the problem is presented above, using a formula to determine the path and magnitude of the force.

If you have any questions

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In this material you will find a detailed description of the law of change in the kinetic energy of a body, which is expressed by the formula W = 9t⁴ J. You will learn how kinetic energy depends on time, and you will also be able to calculate the path traveled by a body over a certain period of time and the magnitude of the force acting on the body at a particular moment in time.

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We present to you a unique digital product - material about the kinetic energy of the body! In this material you will find a detailed description of the law of change in the kinetic energy of a body, which is expressed by the formula W = 9t4 J. You will learn how kinetic energy depends on time, and will also be able to calculate the path traveled by the body in a certain period of time and the magnitude of the force acting on the body at a specific moment in time.

The material is presented in a beautiful html format, which ensures convenience and ease of perception of information. You can easily navigate the text and quickly find the necessary information.

This digital product will become an indispensable assistant for students, teachers and anyone interested in physics and its application in life. You can use it to independently study the material, prepare for exams and write scientific papers.

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Product description:

It is proposed to solve problem 30967, associated with determining the path and magnitude of the force acting on a body, for a given law of change in the kinetic energy of the body.

According to the conditions of the problem, the kinetic energy of the body increases with time according to the law W=9t^4 J, where t is time in seconds. Body weight is 2 kg.

To determine the path traveled by a body during the time period from t1=1s to t2=3s, it is necessary to use the kinetic energy formula:

W = mv^2/2,

where m is the mass of the body, v is the speed of the body.

Since the kinetic energy of a body changes according to the law W=9t^4 J, we can find the speed of the body at time t2:

W2 = 9t2^4 = mv2^2/2

From here you can find the speed v2:

v2 = sqrt(2W2/m) = sqrt(293^4/2) = 27 m/s

The speed v1 at time t1 is found similarly:

v1 = sqrt(2W1/m) = sqrt(291^4/2) = 3 m/s

Then the path traveled by the body during the time from t1 to t2 is calculated:

S = (v2^2 - v1^2)/2a,

where a is the acceleration of the body, which can be found from the law of change in kinetic energy:

W = mv^2/2 = maS

a = 2W/mS = 9t^4/2m

Substituting the found values, we get:

S = (27^2 - 3^2)/(293^4/(2*2)) = 0.335 m

To calculate the magnitude of the force acting on the body at time t2, you can use the formula:

F = ma = m9t^4/2m = 4.5*t^4 H

Substituting t2 = 3 s, we get:

F = 4.5*3^4 = 121.5 N

Thus, the path traveled by the body during the time interval from t1=1s to t2=3s is equal to 0.335 m, and the magnitude of the force applied to the body at time t2 is equal to 121.5 N.

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