Displacement

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 $\int_{a}^{b} v(t) \ dt$.

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?

Related terms

Velocity: The rate of change of position with respect to time; can be integrated to find displacement.

Definite Integral: An integral with upper and lower limits, used to calculate quantities like area under a curve and net change.

Net Change Theorem: A principle stating that the net change over an interval can be found by integrating the rate of change over that interval.