displacement

(noun)

a vector quantity which denotes distance with a directional component

Related Terms

  • trajectory
  • acceleration

Examples of displacement in the following topics:

  • Tangent and Velocity Problems

    • Velocity is defined as rate of change of displacement.
    • The average velocity $\bar{\vec{v}}$ of an object moving through a displacement ($\Delta \vec{x}$) during a time interval ($\Delta t$) is described by the formula: $\displaystyle \bar{\vec{v}} = \frac{\Delta \vec{x}}{\Delta t}$.
    • Slope of tangent of position or displacement time graph is instantaneous velocity and its slope of chord is average velocity.
  • Applications of Second-Order Differential Equations

    • In classical mechanics, a harmonic oscillator is a system that, when displaced from its equilibrium position, experiences a restoring force, $F$, proportional to the displacement, $x$: $\vec F = -k \vec x \,$, where $k$ is a positive constant.
  • Calculus with Parametric Curves

    • The position of the object is given by $x$ and $y$, signifying horizontal and vertical displacement, respectively.
  • Differentiation and Rates of Change in the Natural and Social Sciences

    • For example, in physics, the derivative of the displacement of a moving body with respect to time is the velocity of the body, and the derivative of velocity with respect to time is acceleration.
  • Indefinite Integrals and the Net Change Theorem

    • Such a problem can be solved using the net change theorem, which states that the integral of a rate of change is the net change (displacement for position functions):
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