Formulas

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Created by
Christine

Cards (24)

  • Displacement: Δx=\Delta x=xf−xix_f-x_i
  • Average Velocity (Slope of the Line): vx,aνg=v_{x,a\nu g}=ΔxΔt\frac{\Delta x}{\Delta t}
  • Instantaneous Velocity: vx=v_x=ΔxΔt=\frac{\Delta x}{\Delta t}=dxdt\frac{dx}{dt}
  • Constant Velocity: xf=x_{f}=xt+x_{t}+vxΔt{v}_{x}\Delta t
  • Acceleration: a=a=ΔvΔt\frac{\Delta v}{\Delta t}
  • Average Acceleration: ax,avg=a_{x,avg}=ΔvxΔt\frac{\Delta\boldsymbol{v}_x}{\Delta\boldsymbol{t}}
  • Instantaneous Acceleration: ax=a_x=ΔνxΔt=\frac{\Delta\nu_x}{\Delta t}=dνxdt\frac{d\nu_x}{dt}
  • Constant Acceleration Formulas:
    • vf=v_{f}=vi+v_{i}+axΔta_{x}\Delta t
    • xf=x_{f}=xi+x_{i}+12(vxi+\frac{1}{2}(v_{xi}+vxf)tv_{xf})t
    • vxf2=v_{xf}^{2}=vxi2+v_{xi}^{2}+2ax(xf−xt)2a_{x}(x_{f}-x_{t})
    • xf=x_{f}=xt+x_{t}+vxtt+v_{xt}t+12axt2\frac{1}{2}a_{x}t^{2}
  • Constant Acceleration at initial time = 0: xf=x_{f}=xi+x_{i}+12(vxi+\frac{1}{2}(v_{xi}+vxf)tv_{xf})t
  • Free-Falling Object: vyf=v_{yf}=vyi−gΔtv_{yi}-{g}\Delta t
  • Free-Falling Object at initial time = 0: yf=y_{f}=yi+y_{i}+12(vyi+\frac{1}{2}(v_{yi}+vyf)tv_{yf}){t}
  • Free-Falling Object Formulas (motion is in y and a_y = -g):
    • vyf=v_{yf}=vyt−gΔtv_{yt}-g\Delta t
    • yf=y_{f}=yt+y_{t}+12(vyt+\frac{1}{2}(v_{yt}+vyf)tv_{yf})t
    • vyf2=v_{yf}^{2}=vyi2−2g(yf−yt)v_{yi}^{2}-2g\left(y_{f}-y_{t}\right)
    • yf=y_{f}=yt+y_{t}+vytt−12gt2v_{yt}t-\frac{1}{2}gt^{2}
  • 2-Dimension Motion: r⃗=\vec{{r}}=xi^+x\hat{{i}}+yj^y\hat{{j}}
  • Projectile Motion x-axis:
    • xf=x_{f}=xi+x_{i}+vxitv_{xi}t
    • vxf=v_{xf}=vxiv_{xi}
  • Projectile Motion y-axis:
    • vyf=v_{yf}=vyi−gtv_{yi}-gt
    • yf=y_{f}=yi+y_{i}+12(vyi+\frac{1}{2}(v_{yi}+vyf)tv_{yf})t
    • vyf2=v_{yf}^{2}=vyi2−2g(yf−yi)v_{yi}^{2}-2g(y_{f}-y_{i})
    • yf=y_{f}=yi+y_{i}+vyit−12gt2v_{yi}t-\frac{1}{2}gt^{2}
  • Projectile Motion height: h=h=vi2sin⁡2θi2g\frac{{v_{i}}^{2}\sin^{2}\theta_{i}}{2g}
  • Projectile Motion horizontal range: R=R=vi2sin⁡2θig\frac{{v_i}^2\sin2\theta_i}g
  • Projectile Motion maximum range: Rmax=R_{max}=vi2g\frac{{v_{i}}^{2}}{g}
  • Third Law of Motion: FA=F_A=−FB-F_B
  • Conditions of Static Equilibrium - Forces: ∑F⃗=\sum\vec{F}=00
  • Conditions of Static Equilibrium - Torques: ∑t⃗=\sum\vec{t}=00
  • Translational Equilibrium:
    First Law of Motion: ∑F⃗=\sum\vec{{F}}=00
    ∑F⃗x=\sum\vec{{F}}_{{x}}=0∑F⃗y={0}\quad\sum\vec{{F}}_{{y}}=0∑F⃗z={0}\quad\sum\vec{{F}}_{{z}}=0{0}
  • Rotational Equilibrium:
    • ΣM=\Sigma M=00
    • M=M=FLFL
  • Direction of Moment:
    • +M: counterclockwise
    • -M: clockwise