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Key Equations

Total displacementΔxTotal= ΔxiΔxTotal= Δxi
Average velocity (for constant acceleration)v=ΔxΔt=x2x1t2t1v=ΔxΔt=x2x1t2t1
Instantaneous velocityv(t)=dx(t)dtv(t)=dx(t)dt
Average speedAverage speed=s=Total distanceElapsed timeAverage speed=s=Total distanceElapsed time
Instantaneous speedInstantaneous speed=|v(t)|Instantaneous speed=|v(t)|
Average accelerationa=ΔvΔt=vfv0tft0a=ΔvΔt=vfv0tft0
Instantaneous accelerationa(t)=dv(t)dta(t)=dv(t)dt
Position from average velocityx=x0+vtx=x0+vt
Average velocityv=v0+v2v=v0+v2
Velocity from accelerationv=v0+at(constanta)v=v0+at(constanta)
Position from velocity and accelerationx=x0+v0t+12at2(constanta)x=x0+v0t+12at2(constanta)
Velocity from distancev2=v02+2a(xx0)(constanta)v2=v02+2a(xx0)(constanta)
Velocity of free fallv=v0gt(positive upward)v=v0gt(positive upward)
Height of free fally=y0+v0t12gt2y=y0+v0t12gt2
Velocity of free fall from heightv2=v022g(yy0)v2=v022g(yy0)
Velocity from accelerationv(t)=a(t)dt+C1v(t)=a(t)dt+C1
Position from velocityx(t)=v(t)dt+C2x(t)=v(t)dt+C2
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