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Dynamics Exam 1 Formula Sheet

# Dynamics Exam 1 Formula Sheet - r=r-r(displacement s=s-s...

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Δr=r’-r (displacement) Δs=s’-s Velocity: Inst Vel: v=dr/dt Inst Speed: v=ds/dt Avg Vel: v=Δr/Δt Avg Speed: v=Δs/Δt Acceleration: Vector: a=dv/dt=d 2 r/dt Scalar: a=dv/dt=d 2 s/dt 2 ads=vdv Position: v=ds/dt Constant Accleration v=v o +at s=s o +v o t+.5at 2 v 2 =V o 2 +2a(s-s o ) Graphs Given s-t graph, slope=velocity ds/dt=v Given v-t graph, slope=acc dv/dt=a Δs=∫v dt Given a-t graph, area under line=Δv Δv=∫a dt Given a-s graph .5(v 2 -v o 2 )=∫a ds Given v-s a=v(dv/ds) (velocity*slope) Rectangular Components r= x i+ y j+ z k v=v x i+v y j+v z k v x =x(dot) v y =y(dot) v z =z(dot) acceleration is double dot Horizontal Projectile v=v o +at vx=v o x x=x o +v o t+.5at 2 v 2 =v o 2 +2a(s-s o ) Vertical Projectile v=v o +at / v=v o -gt y=y o +v o t+.5at 2 / y=y o +v o t-.5gt 2 v 2 =v o 2 +2a(y-y o ) / v 2 =V o 2 -2g(y-y o ) Normal & Tangential Components v=ds/dt(u(t))=s(dot)*u(t)=v*u(t)
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