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A force only performs Work if there is displacement of the body on which it acts. That way, if a person at rest holds an object, he is not doing Work. Analyzing this way, we can relate these events to the following mathematical equation for the Work performed by a force: , where τ (Greek letter tau) = work, F = force and d = displacement.

In some situations the work is done more quickly. For example, a marathon course was taken by two people at different times. In this case, we say that the person who completed the route in less time developed a higher average power in relation to another person. Based on this definition, the mathematical equation responsible for calculating the power of a body is given by the expression: , where ∆t: time variation.

*Example 1*

Determine the work done by a force of intensity 250 N (Newton) applied to a body, which moves for 20 meters in the same direction as the force.

τ = F * d

τ = 250 * 20

τ = 5000 N/m

τ = 5000 J (joule)

*Example 2*

A force of 40 N intensity is applied to a body, displacing it for 5 meters in the direction and direction of the force, for 10 seconds. Based on this information calculate:

a) the work performed by force.

b) the average power of this force.

a) τ = F * d

τ = 40 * 5

τ = 200 N/m

τ = 200 J (joule)

B)

by Mark Noah

Graduated in Mathematics

Brazil School Team

**Equations** - **Math** - **Brazil School**

**Source:** Brazil School - https://brasilescola.uol.com.br/matematica/equacoes-matematicas-relacionadas-ao-trabalho-potencia-.htm