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4º 5ª
1 km=1000 m1 h=3600 s1 km/h=3.6 m/s1 km/h2=12960 m/s2\begin{aligned} 1 \unit{km} &= 1000 \unit{m} \\ 1 \unit{h} &= 3600 \unit{s} \\ 1 \unit{km/h} &= 3.6 \unit{m/s} \\ 1 \unit{km/h}^2 &= 12960 \unit{m/s}^2 \\ \end{aligned} x=b±b24ac2ax=\frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

#Horinzontalidad

#MRU & MRUV

x=v0t+12t2v1=v0+atv12=v02+2aΔx\begin{aligned} x &= v_0t + \frac{1}{2}t^2 \\ v_1 &= v_0 + at \\ v_1^2 &= v_0^2 + 2a\Delta{x} \\ \end{aligned}

#Verticalidad

G=10 m/s2=129600 km/h2G = -10 \unit{m/s}^2 = -129600 \unit{km/h}^2

#Tiro Vertical

y=v0t+12Gt2v1=v0+Gtv12=v02+2GΔy\begin{aligned} y &= v_0t + \frac{1}{2}Gt^2 \\ v_1 &= v_0 + Gt \\ v_1^2 &= v_0^2 + 2G\Delta{y} \\ \end{aligned}

#Caida Libre

y1=y0+12Gt2v=Gtv2=2GΔy\begin{aligned} y_1 &= y_0 + \frac{1}{2}Gt^2 \\ v &= Gt \\ v^2 &= 2G\Delta{y} \end{aligned}

#Fuerza

1 N=1 kg×m/s21 kgf=10 N\begin{aligned} 1 \unit{N} &= 1 \unit{kg×m/s}^2 \\ 1 \unit{kgf} &= 10 \unit{N} \end{aligned} F=maP=mG\begin{aligned} F &= ma \\ P &= mG \end{aligned}
  • Fuerza elástica: Fe=kΔxF_e = k \Delta x
  • Rozamiento

    • Estático: FreμeNF_{re} \leq \mu_eN
    • Dinámico: Frd=μdNF_{rd} = \mu_dN

#Energía y trabajo

1 J=1 N×1 m1 kgf×m=1 kgm=9,807 J\begin{aligned} 1 \unit{J} &= 1 \unit{N} × 1 \unit{m} \\ 1 \unit{kgf×m} = 1 \unit{kgm} &= 9,807 \unit{J} \\ \end{aligned} Ec=mv22J=ΔEc=mv122mv022\begin{aligned} E_c &= \frac{mv^2}{2} \\ J = \Delta{E_c} &= \frac{mv^2_1}{2} - \frac{mv^2_0}{2} \end{aligned} Epg=GMmhmhGEpe=k(Δx)22J=Ep AEp B\begin{aligned} E_{pg} &= -G\frac{Mm}{h} \approx mh|G| \\ E_{pe} &= \frac{k(\Delta{x})^2}{2} \\ J &= E_p\ A - E_p\ B \end{aligned}

#Potencia

1 W (Watt)=1 J/s1 kW=1000 J/s=101,97 kg×m/s=1,341 cv=1,256 hp1 kW×h=3.600.000 J\begin{aligned} 1 \unit{W (Watt)} &= 1 \unit{J/s} \\ 1 \unit{kW} &= 1000 \unit{J/s} \\ &= 101,97 \unit{kg×m/s} \\ &= 1,341 \unit{cv} \\ &= 1,256 \unit{hp} \\ 1 \unit{kW×h} &= 3.600.000 \unit{J} \end{aligned} P=JsP = \frac{\text{J}}{\text{s}}