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Displacement

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Calculus II

Definition

Displacement is the net change in position of an object, calculated as the integral of velocity over a given time interval. It can be represented mathematically as $\int_{a}^{b} v(t) \ dt$.

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5 Must Know Facts For Your Next Test

  1. In calculus, displacement is found using the definite integral of a velocity function.
  2. The limits of integration represent the time interval during which the displacement is measured.
  3. Displacement considers direction, making it different from distance, which only considers magnitude.
  4. If the velocity function $v(t)$ changes sign within the interval, it indicates that the object has changed direction.
  5. The Fundamental Theorem of Calculus links differentiation and integration, helping to compute displacement from velocity.

Review Questions

  • What is the mathematical representation for calculating displacement using integration?
  • How does displacement differ from distance in terms of calculus?
  • What does it imply if the velocity function changes sign within an interval?

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