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Key Equations

Position vector r(t)=x(t)i^+y(t)j^+z(t)k^r(t)=x(t)i^+y(t)j^+z(t)k^
Displacement vector Δr=r(t2)r(t1)Δr=r(t2)r(t1)
Velocity vector v(t)=limΔt0r(t+Δt)r(t)Δt=drdtv(t)=limΔt0r(t+Δt)r(t)Δt=drdt
Velocity in terms of components v(t)=vx(t)i^+vy(t)j^+vz(t)k^v(t)=vx(t)i^+vy(t)j^+vz(t)k^
Velocity components vx(t)=dx(t)dtvy(t)=dy(t)dtvz(t)=dz(t)dtvx(t)=dx(t)dtvy(t)=dy(t)dtvz(t)=dz(t)dt
Average velocity vavg=r(t2)r(t1)t2t1vavg=r(t2)r(t1)t2t1
Instantaneous acceleration a(t)=limt0v(t+Δt)v(t)Δt=dv(t)dta(t)=limt0v(t+Δt)v(t)Δt=dv(t)dt
Instantaneous acceleration, component form a(t)=dvx(t)dti^+dvy(t)dtj^+dvz(t)dtk^a(t)=dvx(t)dti^+dvy(t)dtj^+dvz(t)dtk^
Instantaneous acceleration as second
derivatives of position
Time of flight Ttof=2(v0sinθ0)gTtof=2(v0sinθ0)g
Trajectory y=(tanθ0)x[g2(v0cosθ0)2]x2y=(tanθ0)x[g2(v0cosθ0)2]x2
Range R=v02sin2θ0gR=v02sin2θ0g
Centripetal acceleration aC=v2raC=v2r
Position vector, uniform circular motion r(t)=Acosωti^+Asinωtj^r(t)=Acosωti^+Asinωtj^
Velocity vector, uniform circular motion v(t)=dr(t)dt=Aωsinωti^+Aωcosωtj^v(t)=dr(t)dt=Aωsinωti^+Aωcosωtj^
Acceleration vector, uniform circular motion a(t)=dv(t)dt=Aω2cosωti^Aω2sinωtj^a(t)=dv(t)dt=Aω2cosωti^Aω2sinωtj^
Tangential acceleration aT=d|v|dtaT=d|v|dt
Total acceleration a=aC+aTa=aC+aT
Position vector in frame
S is the position
vector in frame SS plus the vector from the
origin of S to the origin of SS
Relative velocity equation connecting two
reference frames
Relative velocity equation connecting more
than two reference frames
Relative acceleration equation aPS=aPS+aSSaPS=aPS+aSS
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