Terms
Table of Contents
- Kinematics
- Inertia
- Translation
- Position
- Reference Frame
- Distance
- Displacement
- Speed
- Instantaneous Speed
- Velocity
- Instantaneous Velocity
- Acceleration
- References
- Kinematics
- Second Law of Motion
- Second Law of Motion
- Uniform Motion
- Uniformly Accelerated Motion
- Velocity
- Uniform Motion
- Inertial Frames of Reference
- Projectile Motion
- Relative Velocity
- Uniform Motion
- Accelerated Motion
- Uniformly Accelerated Motion
- Velocity
- Instantaneous Velocity
- Acceleration
- Velocity
- Velocity
- Velocity
- Work
- Uniform Motion
- Velocity
- Speed
- First Law of Motion
- Kinematics
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.
- it is a scalar quantity.
Displacement
- Displacement x refers to straight-line distance between it initial and final
positions, with direction toward the final position.
- it is a vector quantity.
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
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:
- \(x\) is displacement
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
Formula
\begin{align*}
& a = \frac{d}{dt}(\vec{v}) \\
& a = \frac{d^2x}{dt^2} \\
& A = \frac{velocity}{time}
\end{align*}