Terms

Table of Contents

Kinematics

  • Kinematics is a quantitative description of motion without reference to its physical causes.

Inertia

  • the capacity of an object to resist changes in motion.
  • resistance to motion.
  • proportional to the mass of an object.
  • more mass \(\propto\) more inertia

Translation

  • Translation is the physical term for straight-line motion.

Position

  • Position refers to the location of an object with respect to some reference frame.

Reference Frame

  • Reference frame is a physical entity to which motion or position of an object is being referred.

Distance

  • Distance d refers to the actual length of path taken by an object in which moving from its initial position to its final position.

Displacement

  • Displacement x refers to straight-line distance between it initial and final positions, with direction toward the final position.

Formula

\begin{align*} & \Delta x = \left(\frac{v_i + v_f}{2}\right)\Delta t,\ \text{only true when acceleration is constant}\\ & x = \iint \vec{a}\, dt\, dt \\ & x = \int\vec{v}\, dt \end{align*}

Speed

  • Speed is the distance that a body moves in a unit time.
  • Since distance is scalar quantity. Speed is also a scalar quantity.

Formula

\begin{align*} & s = \frac{d}{t} \\ & s = \frac{d}{dt}(l) \end{align*}
  • where \(l\) is the length of path or distance.

Instantaneous Speed

  • The instantaneous speed of an object is its speed at a particular instant of time, with it being extremely small.
  • The speed indicated by a speedometer is instantaneous speed.

Velocity

  • When the speed of a body is associated with a direction, the result is the velocity of the body.
  • Velocity is vector quantity.
  • The speed of the body is the magnitude of its velocity.
  • The SI Unit for speed and velocity is meter per second, m/s.
  • Average velocity is total displacement divided by total time.
  • It can change in 3 ways: change in speed (increase or decrease), change in direction, change in speed as well as direction.
  • The derivative of velocity with respect to time is acceleration.

Formula

  • Other formulas that we may use in certain cases:
\begin{align*} & v = \frac{\Delta x}{\Delta t} \\ & v = \frac{v_i + v_f}{2}\ \text{only true when acceleration is constant} \\ & v = \frac{total\ displacement}{total\ time} \end{align*}

Instantaneous Velocity

  • Instantaneous velocity is the velocity at an instant of time.

Formula

\begin{align*} & v = \int \vec{a}\, dt \\ & v = \frac{dx}{dt} \\ \end{align*}

Acceleration

  • Acceleration is change in velocity with respect to time.
  • It is also a vector quantity.
  • The SI Unit of acceleration is meter per second per second, m/s/s or \(m/s^2\)

Formula

\begin{align*} & a = \frac{d}{dt}(\vec{v}) \\ & a = \frac{d^2x}{dt^2} \\ & A = \frac{velocity}{time} \end{align*}

References

Kinematics

Uniform Motion

  • (Motion in a Straight Line > Uniform Motion)

Uniformly Accelerated Motion

  • (Motion in a Straight Line > Uniformly Accelerated Motion)

Uniform Motion

  • (Motion in a Straight Line > Uniform Motion)

Inertial Frames of Reference

  • (First Law of Motion > Inertial Frames of Reference)

Uniform Motion

  • (Motion in a Straight Line > Uniform Motion)

Accelerated Motion

  • (Motion in a Straight Line > Accelerated Motion)

Uniformly Accelerated Motion

  • (Motion in a Straight Line > Uniformly Accelerated Motion)

Uniform Motion

  • (Motion in a Straight Line > Uniform Motion)

Velocity

  • (Velocity > Formula)

Date: August 16, 2023

Author: Paul Gerald D. Pare

Emacs 29.1 (Org mode 9.6.6)