University Physics Volume 1

# Key Equations

### Key Equations

 Displacement $Δx=xf−xiΔx=xf−xi$ Total displacement $ΔxTotal=∑ ΔxiΔxTotal=∑ Δxi$ Average velocity (for constant acceleration) $v–=ΔxΔt=x2−x1t2−t1v–=ΔxΔt=x2−x1t2−t1$ Instantaneous velocity $v(t)=dx(t)dtv(t)=dx(t)dt$ Average speed $Average speed=s–=Total distanceElapsed timeAverage speed=s–=Total distanceElapsed time$ Instantaneous speed $Instantaneous speed=|v(t)|Instantaneous speed=|v(t)|$ Average acceleration $a–=ΔvΔt=vf−v0tf−t0a–=ΔvΔt=vf−v0tf−t0$ Instantaneous acceleration $a(t)=dv(t)dta(t)=dv(t)dt$ Position from average velocity $x=x0+v–tx=x0+v–t$ Average velocity $v–=v0+v2v–=v0+v2$ Velocity from acceleration $v=v0+at(constanta)v=v0+at(constanta)$ Position from velocity and acceleration $x=x0+v0t+12at2(constanta)x=x0+v0t+12at2(constanta)$ Velocity from distance $v2=v02+2a(x−x0)(constanta)v2=v02+2a(x−x0)(constanta)$ Velocity of free fall $v=v0−gt(positive upward)v=v0−gt(positive upward)$ Height of free fall $y=y0+v0t−12gt2y=y0+v0t−12gt2$ Velocity of free fall from height $v2=v02−2g(y−y0)v2=v02−2g(y−y0)$ Velocity from acceleration $v(t)=∫a(t)dt+C1v(t)=∫a(t)dt+C1$ Position from velocity $x(t)=∫v(t)dt+C2x(t)=∫v(t)dt+C2$