Formulas

• Displacement: $\Delta x=$$x_f-x_i$
• Average Velocity (Slope of the Line): $v_{x,a\nu g}=$$\frac{\Delta x}{\Delta t}$
• Instantaneous Velocity: $v_x=$$\frac{\Delta x}{\Delta t}=$$\frac{dx}{dt}$
• Constant Velocity: $x_{f}=$$x_{t}+$${v}_{x}\Delta t$
• Acceleration: $a=$$\frac{\Delta v}{\Delta t}$
• Average Acceleration: $a_{x,avg}=$$\frac{\Delta\boldsymbol{v}_x}{\Delta\boldsymbol{t}}$
• Instantaneous Acceleration: $a_x=$$\frac{\Delta\nu_x}{\Delta t}=$$\frac{d\nu_x}{dt}$
• Constant Acceleration Formulas:

  • $v_{f}=$$v_{i}+$$a_{x}\Delta t$
  • $x_{f}=$$x_{i}+$$\frac{1}{2}(v_{xi}+$$v_{xf})t$
  • $v_{xf}^{2}=$$v_{xi}^{2}+$$2a_{x}(x_{f}-x_{t})$
  • $x_{f}=$$x_{t}+$$v_{xt}t+$$\frac{1}{2}a_{x}t^{2}$
• Constant Acceleration at initial time = 0: $x_{f}=$$x_{i}+$$\frac{1}{2}(v_{xi}+$$v_{xf})t$
• Free-Falling Object: $v_{yf}=$$v_{yi}-{g}\Delta t$
• Free-Falling Object at initial time = 0: $y_{f}=$$y_{i}+$$\frac{1}{2}(v_{yi}+$$v_{yf}){t}$
• Free-Falling Object Formulas (motion is in y and a_y = -g):

  • $v_{yf}=$$v_{yt}-g\Delta t$
  • $y_{f}=$$y_{t}+$$\frac{1}{2}(v_{yt}+$$v_{yf})t$
  • $v_{yf}^{2}=$$v_{yi}^{2}-2g\left(y_{f}-y_{t}\right)$
  • $y_{f}=$$y_{t}+$$v_{yt}t-\frac{1}{2}gt^{2}$
• 2-Dimension Motion: $\vec{{r}}=$$x\hat{{i}}+$$y\hat{{j}}$
• Projectile Motion x-axis:

  • $x_{f}=$$x_{i}+$$v_{xi}t$
  • $v_{xf}=$$v_{xi}$
• Projectile Motion y-axis:

  • $v_{yf}=$$v_{yi}-gt$
  • $y_{f}=$$y_{i}+$$\frac{1}{2}(v_{yi}+$$v_{yf})t$
  • $v_{yf}^{2}=$$v_{yi}^{2}-2g(y_{f}-y_{i})$
  • $y_{f}=$$y_{i}+$$v_{yi}t-\frac{1}{2}gt^{2}$
• Projectile Motion height: $h=$$\frac{{v_{i}}^{2}\sin^{2}\theta_{i}}{2g}$
• Projectile Motion horizontal range: $R=$$\frac{{v_i}^2\sin2\theta_i}g$
• Projectile Motion maximum range: $R_{max}=$$\frac{{v_{i}}^{2}}{g}$
• Third Law of Motion: $F_A=$$-F_B$
• Conditions of Static Equilibrium - Forces: $\sum\vec{F}=$$0$
• Conditions of Static Equilibrium - Torques: $\sum\vec{t}=$$0$
• Translational Equilibrium:

  First Law of Motion: $\sum\vec{{F}}=$$0$

  $\sum\vec{{F}}_{{x}}=$${0}\quad\sum\vec{{F}}_{{y}}=$${0}\quad\sum\vec{{F}}_{{z}}=$${0}$
• Rotational Equilibrium:

  • $\Sigma M=$$0$
  • $M=$$FL$
• Direction of Moment:

  • +M: counterclockwise
  • -M: clockwise