Physics Kinematics, Dynamics, and Motion Rules Flashcards

Comprehensive vocabulary flashcards covering 1D kinematics, free fall, projectile motion, Newton's laws, forces, proportionality, significant figures, and unit conversions based on the provided physics notes.

Total Distance

Sum of all paths traveled (scalar), given by $d_T = A + B + \dots + n$.

Vector Displacement Sum

Directional vector addition, given by $\vec{d}_R = \vec{d}_A + \vec{d}_B$.

Resultant Displacement

Straight-line distance between start and end (vector), calculated as $\vec{d}_R = \sqrt{a^2 + b^2}$.

Direction Angle

Angle of resultant vector, calculated as $\theta = \tan^{-1}\left(\frac{\text{opp}}{\text{adj}}\right)$.

Average Speed

Total distance divided by total time ($v_{\text{ave}} = \frac{d_T}{t}$).

Average Velocity

Displacement divided by total time dr divided by t

Acceleration

Change in velocity over time interval, calculated as $a = \frac{\Delta v}{\Delta t} = \frac{v_f - v_i}{\Delta t}$.

Final Velocity Equation (no $d$)

Velocity after time $t$ under constant acceleration, given by $v_f = v_i + a\Delta t$.

Initial Velocity Shortcut

Solves directly for $v_i$, given by $v_i = v_f - a\Delta t$.

Time Shortcut

Solves directly for time interval, given by $t = \frac{v_f - v_i}{a}$.

Displacement Equation (no $a$)

Use when acceleration is omitted, given by $d = \left(\frac{v_f + v_i}{2}\right)\Delta t$.

Displacement Equation (no $v_f$)

Distance traveled given $v_i$, $a$, and $t$, calculated as $d = v_i \Delta t + \frac{1}{2}a(\Delta t)^2$.

Final Velocity Squared Equation (no $t$)

Relates initial/final speeds, acceleration, and distance, given by $v_f^2 = v_i^2 + 2ad$.

Final Velocity Root Shortcut

Direct extraction of $v_f$ when $t$ is missing, given by $v_f = \sqrt{v_i^2 + 2ad}$.

Vertical Final Velocity

Speed under gravitational force ($g = -9.8\,m/s^2$), given by $v_f = v_i + g\Delta t$.

Vertical Average Displacement

Distance given initial and final vertical speeds, calculated as $d_y = \left(\frac{v_f + v_i}{2}\right)\Delta t$.

Vertical Displacement

Distance given initial upward/downward velocity, calculated as $d_y = v_i \Delta t + \frac{1}{2}g(\Delta t)^2$.

Vertical Motion without Time

Connects vertical drop distance to speed change, given by $v_f^2 = v_i^2 + 2gd_y$.

Dropped Object Distance

Fall distance from rest ($v_i = 0$), calculated as $d_y = \frac{1}{2}g(\Delta t)^2$.

Dropped Object Velocity

Speed after dropping for time $t$ from rest ($v_i = 0$), calculated as $v_f = g\Delta t$.

Fall Time

Time needed to fall a vertical distance $d_y$, calculated as $t = \sqrt{\frac{2d_y}{g}}$.

Thrown Downward Final Speed

Downward impact speed ($v_f < 0$), calculated as $v_f = -\sqrt{v_i^2 + 2gd_y}$.

Time to Peak ($t_{\text{up}}$)

Time needed to reach top apex ($v_{\text{peak}} = 0$), given by $t_{\text{up}} = \frac{v_f - v_i}{g} = \frac{0 - v_i}{-9.8}$.

Total Flight Time ($t_T$)

Airborne duration for symmetric launches, given by $t_T = 2 \times t_{\text{up}}$.

Apex Peak Height

Calculates peak height given launch velocity and flight time using $d_y = v_i \Delta t + \frac{1}{2}gt^2$.

Horizontal Distance (X-axis)

Motion at constant horizontal speed, calculated as $d_x = v_x \cdot t$.

Vertical Distance Drop (Y-axis)

Free fall drop calculation given by $d_y = \frac{1}{2}gt^2$.

Vertical Velocity Component ($v_y$)

Instantaneous vertical speed at time $t$, calculated as $v_y = gt$.

Horizontal Launch Time

Airborne time based on release height, given by $t = \sqrt{\frac{2d_y}{g}}$.

Peak Height (Angled Launch)

Maximum vertical elevation for an angled launch, given by $d_y = \frac{-(v_i \cdot \sin(\theta))^2}{2g}$.

Total Airborne Time (Angled Launch)

Total duration in air for an angled launch, given by $t_T = (2) \cdot \frac{-v_i \cdot \sin(\theta)}{g}$.

Horizontal Range (Angled Launch)

Overall horizontal landing distance for an angled launch, given by $d_x = v_i \cdot \cos(\theta) \cdot t_T$.

Maximum Range Angle

Direct launch angle for furthest travel, given by $\theta = 45^\circ$.

Net Force Summation

Vector sum of all forces acting on an object, written as $F_{\text{net}} = F_1 + F_2 + F_3 + \dots + F_n$.

Net Force Equation

Total mass multiplied by acceleration, written as $F_{\text{net}} = ma$.

Acceleration (Dynamics)

Net force divided by mass, given by $a = \frac{F_{\text{net}}}{m}$.

Mass (Dynamics)

Net force divided by acceleration, given by $m = \frac{F_{\text{net}}}{a}$.

Weight Force ($W$)

Mass times gravitational acceleration ($W = mg$), where $g = -9.8\,m/s^2$ or $-1.63\,m/s^2$.

Mass from Weight

Weight divided by gravity, calculated as $m = \frac{W}{g}$.

X-Axis Force Summation

Net horizontal force components, given by $F_{\text{net},x} = F_N + F_g$.

Y-Axis Force Summation

Net vertical force components, given by $F_{\text{net},y} = ma$.

Applied vs. Friction

Applied force minus frictional resistance, given by $F_{\text{net},x} = F_{\text{app}} - F_{\text{fric}}$.

Newton's 3rd Law

Action-reaction forces are equal in magnitude and opposite in direction ($F_{\text{car on bug}} = F_{\text{bug on car}}$). Lighter objects accelerate faster due to lower mass.

Proportionality Rules

Direct ($\uparrow\uparrow$ or $\downarrow\downarrow$): Doubling force doubles acceleration ($2a$). Inverse ($\uparrow\downarrow$ or $\downarrow\uparrow$): Doubling mass halves acceleration ($\frac{1}{2}a$).

Sig Figs Rules

Front zeros = NO ($0.005 \rightarrow 1$). End zeros without dot = NO ($500 \rightarrow 1$). End zeros with dot = YES ($500.0 \rightarrow 4$). In-between zeros = YES.

Unit Conversions (Time)

Minutes to seconds $\rightarrow \times 60$ | Seconds to minutes $\rightarrow \div 60$.