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\begin{document}

\frame{\frametitle{\b Work and Energy I-1} \bigskip

{\bf Work-Kinetic Energy (1):} Convert units to $kJ$. 
$$ E_k = \frac{1}{2}\,m\,v^2\,.$$
Should $E_k$ be entered as a positive or negative quantity?
\bigskip

{\bf Horse Power (2):} Convert units to $kJ$ and $W$ (Watt, not to 
be confused with $W$ for work).
$$ W = F_x\,L\,,~~~P_{av} = \frac{W}{t}\,.$$
% \bigskip

{\bf Cartesian dot product (3):} 
$$ W=F_x\,\triangle R_x+F_y\,\triangle R_y+F_z\,\triangle R_z\,.$$
\bigskip

{\bf Work done by a variable force (4):} $\int_0^{x_0} F\,dx\,. $

\vskip 20pt }

\frame{\frametitle{\b Work and Energy I-2} \bigskip

{\bf Force from a position graph (5).}  \bigskip

One segment $x_i\to x_{i+1}$:
$$ W_i = F_i\,(x_{i+1}-x_i) + \frac{1}{2}\,(F_{i+1}-F_i)\,(x_{i+1}-x_i)
   ~~{\rm and}~~W=\sum_i W_i\,. $$ % \bigskip

Velocity:
$$ W = \frac{1}{2}\,m\,\left(v_f^2-v_i^2\right)\,.$$
\bigskip

{\bf Block-spring (6):} 
$$ W = \frac{k}{2}\,x^2 = F_{\mu_k}\,\triangle x\,. $$

{\bf Bungee Cord (7):} 
$$ W = - \int_0^{L_0} F\,dx\,.     $$
\vskip 20pt }

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