acceleration

(noun)

the change of velocity with respect to time (can include deceleration or changing direction)

Related Terms

Examples of acceleration in the following topics:

  • Higher Derivatives

    • The second derivative of $x$ is the derivative of $x'(t)$, the velocity, and by definition is the object's acceleration.
    • Acceleration is the time-rate of change of velocity, and the second-order rate of change of position.

  • Planetary Motion According to Kepler and Newton

    • Newton derived his theory of the acceleration of a planet from Kepler's first and second laws.
    • In addition, the magnitude of the acceleration is inversely proportional to the square of its distance from the Sun.
    • From this, Newton defined the force acting on a planet as the product of its mass and acceleration.

  • Physics and Engineering: Fluid Pressure and Force

    • For fluids near the surface of the earth, the formula may be written as $p = \rho g h$, where $p$ is the pressure, $\rho$ is the density of the fluid, $g$ is the gravitational acceleration, and $h$ is the depth of the liquid in meters.

  • Calculus with Parametric Curves

    • The acceleration can be written as follows with the double apostrophe signifying the second derivative:

  • Vectors in Three Dimensions

    • Vectors play an important role in physics: velocity and acceleration of a moving object and forces acting on it are all described by vectors.

  • 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.

  • Vector-Valued Functions

    • If we differentiate a second time, we will be left with acceleration:

  • Arc Length and Curvature

    • Where $\kappa$ is the curvature and $\frac{dT}{ds}$ is the acceleration vector (the rate of change of the velocity vector over time).

  • Graphing on Computers and Calculators

    • c) Three-dimensional graphing: While high-end graphing calculators can graph in 3-D, GraphCalc benefits from modern computers' memory, speed, and graphics acceleration.