displacement

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):