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Kinematics definitions

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  • Displacement

    Change in location found by integrating the velocity function over a time interval; can be positive or negative depending on direction.
  • Total Distance

    Sum of all movement, calculated by integrating the absolute value of velocity to ensure only positive values are included.
  • Position Function

    Expression giving location at any time, found by integrating velocity and adding the initial location.
  • Velocity Function

    Expression describing rate of change of location, obtained by integrating acceleration and including the initial rate.
  • Acceleration Function

    Expression representing the rate of change of velocity, often given as a function of time.
  • Initial Position

    Starting location value used as a constant when constructing the position function.
  • Initial Velocity

    Starting rate of change of position, used as a constant when constructing the velocity function.
  • Definite Integral

    Mathematical tool for finding accumulated change, such as area under a curve, between two bounds.
  • Antiderivative

    Function whose derivative yields the original function; used to reverse differentiation in motion problems.
  • Dummy Variable

    Placeholder symbol in integration, ensuring the resulting function is expressed in terms of the desired variable.
  • Area Under the Curve

    Graphical representation of accumulated change, such as displacement or total distance, found via integration.
  • Absolute Value

    Operation ensuring all values are non-negative, crucial for calculating total distance from velocity.
  • Time Interval

    Span between two time points over which integration is performed to find displacement or distance.
  • Power Rule

    Technique for finding antiderivatives, especially useful when integrating polynomial functions in motion problems.
  • Units

    Measurement labels, such as meters or seconds, that clarify the physical meaning of position, velocity, and acceleration.