Important Physical Relationships in Kinematics

Vocabulary flashcards defining fundamental kinematic concepts, quantities, and mathematical relationships for general, rectilinear, and circular motion.

Definition Symbol (\stackrel{\text{def}}{=})

A symbol indicating that the expression defines the quantity on the left side, rather than representing a physical law.

Delta Symbol (\Delta)

A symbol used in high school physics to represent a sufficiently small change or interval of a quantity, such as time interval $\Delta t$ or area $\Delta S$.

Instantaneous Velocity (v)

The rate of change of the position vector over a small time interval, defined as $v \stackrel{\text{def}}{=} \frac{\Delta r}{\Delta t}$.

Instantaneous Acceleration (a)

The rate of change of velocity over a small time interval, defined as $a \stackrel{\text{def}}{=} \frac{\Delta v}{\Delta t}$.

Average Speed (v_p)

The ratio of total distance $s$ traveled to total time $t$, defined as $v_p \stackrel{\text{def}}{=} \frac{s}{t}$.

Average Acceleration (a_p)

The ratio of velocity increase $v_2 - v_1$ to time interval $t$, defined as $a_p \stackrel{\text{def}}{=} \frac{v_2 - v_1}{t}$.

Uniform Rectilinear Motion - Distance Formula

The distance traveled over time $t$ when acceleration $a = 0$ and velocity $v = \text{const.}$, given by $s(t) = vt$.

Uniform Rectilinear Motion - Position Formula

The position at time $t$ given an initial position $x_0$, expressed as $x(t) = x_0 + vt$.

Uniformly Accelerated Rectilinear Motion - Velocity Formula

The velocity at time $t$ under constant acceleration $a \neq 0$, given by $v(t) = v_0 + at$ where $v_0$ is initial velocity.

Uniformly Accelerated Rectilinear Motion - Position Formula

The position at time $t$ under constant acceleration $a$, given by $x(t) = x_0 + v_0 t + \frac{1}{2} a t^2$.

Uniformly Accelerated Rectilinear Motion - Average Velocity

The average velocity over a time interval with initial velocity $v_1$ and final velocity $v_2$, given by $v_p = \frac{1}{2} (v_1 + v_2)$.

Rectilinear Motion Starting from Rest at Origin - Velocity

The instantaneous velocity at time $t$ for motion starting from rest at the origin, given by $v(t) = at$.

Rectilinear Motion Starting from Rest at Origin - Distance

The distance covered in time $t$ for motion starting from rest at the origin, given by $s(t) = \frac{1}{2} a t^2$.

Speed-Distance Relation from Rest

The speed magnitude at a distance $s$ from the origin when starting from rest with constant acceleration $a$, given by $v = \sqrt{2as}$.

Circular Arc Distance (s)

The distance traveled along a circular path of radius $r$, calculated as $s = r \varphi$ where $\varphi$ is the angle in radians.

Instantaneous Angular Velocity (\omega)

The rate of change of angle over time, defined as $\omega \stackrel{\text{def}}{=} \frac{\Delta \varphi}{\Delta t}$ or $\omega = \frac{v}{r}$.

Instantaneous Angular Acceleration (\alpha)

The rate of change of angular velocity over time, defined as $\alpha \stackrel{\text{def}}{=} \frac{\Delta \omega}{\Delta t}$.

Centripetal Acceleration (a_d)

The acceleration directed toward the center of a circular trajectory, given by $a_d = \omega^2 r = \frac{v^2}{r}$.

Uniform Circular Motion - Angular Displacement

The angle at time $t$ for motion with constant angular velocity $\omega$, given by $\varphi(t) = \omega t + \varphi_0$ where $\varphi_0$ is the initial angle.

Uniform Circular Motion - Angular Velocity via Period and Frequency

The angular velocity expressed using orbital period $T$ and rotation frequency $f$, given by $\omega = \frac{2\pi}{T} = 2\pi f$.

Uniform Circular Motion - Linear Speed Relationships

The magnitude of velocity in circular motion expressed via period $T$, frequency $f$, and radius $r$, given by $v = \frac{2\pi r}{T} = 2\pi r f = \omega r$.

1D Vector Component Sign Convention

In straight-line motion formulas, symbols $a$, $v$, and $x$ denote vector components along the line; a negative value indicates that the vector points to the left.