How Much Work Does a Machine Perform Between 9s and 18s?

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SUMMARY

The discussion focuses on calculating the work done by a machine operating at a power rate defined by the equation P = ct², where c is 18 W/s². To find the work done between 9.0 seconds and 18 seconds, the integral of power with respect to time must be computed. The relationship P = dW/dt indicates that integrating power over the specified time interval yields the total work done. This approach is essential for solving problems involving variable power rates.

PREREQUISITES
  • Understanding of calculus, specifically integration techniques.
  • Familiarity with the concepts of power and work in physics.
  • Knowledge of the relationship between power, work, and time.
  • Ability to manipulate and solve equations involving variables.
NEXT STEPS
  • Learn integration techniques for variable functions in calculus.
  • Study the relationship between power, work, and energy in physics.
  • Explore practical applications of power equations in engineering contexts.
  • Review examples of calculating work done by machines with varying power outputs.
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Students in physics or engineering courses, educators teaching mechanics, and anyone interested in understanding the principles of work and power in mechanical systems.

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Homework Statement


A machine does work at a rate given by , P=ct^2 where c= 18 W/s^2 and t is time.
Find the work done by the machine between 9.0s and 18s .

Homework Equations



P=w/t

The Attempt at a Solution



no ideas
 
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pph1011 said:

Homework Statement


A machine does work at a rate given by , P=ct^2 where c= 18 W/s^2 and t is time.
Find the work done by the machine between 9.0s and 18s .

Homework Equations



P=w/t

The Attempt at a Solution



no ideas

Integrate with respect to time because:

[tex]P=\frac{dW}{dt}[/tex].
 

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