Generated by the Physics Derivation Graph. Eq. \ref{eq:2237799} is an initial equation. $$dW = F dx \label{eq:2237799}$$ Integrate Eq.~ref{eq:2237799}; yields Eq.~ref{eq:2565189}. $$\int dW = F \int_0^x dx \label{eq:2565189}$$ Evaluate definite integral Eq. \ref{eq:2565189}; yields Eq. \ref{eq:7362045}. $$W = F x \label{eq:7362045}$$ Substitute LHS of Eq. \ref{eq:7362045} into Eq. \ref{eq:3086821}; yields Eq. \ref{eq:6167182}. $$W = m a x \label{eq:6167182}$$ Change of variable $$d$$ to $$x$$ and $$v$$ to $$v_2$$ and $$v$$ to $$v_1$$ in Eq. \ref{eq:4741344}; yields Eq. \ref{eq:5997798}. $$x = \frac{v_2^2 - v_1^2}{2 a} \label{eq:5997798}$$ Substitute LHS of Eq. \ref{eq:5997798} into Eq. \ref{eq:6167182}; yields Eq. \ref{eq:6760874}. $$W = m a \frac{v_2^2 - v_1^2}{2 a} \label{eq:6760874}$$ Simplify Eq. \ref{eq:6760874}; yields Eq. \ref{eq:4236963}. $$W = \frac{1}{2} m v_2^2 - \frac{1}{2} m v_1^2 \label{eq:4236963}$$ Substitute LHS of Eq. \ref{eq:8207477} and LHS of Eq. \ref{eq:8883350} into Eq. \ref{eq:4236963}; yields Eq. \ref{eq:4943050}. $$W = KE_2 - KE_1 \label{eq:4943050}$$ Eq. \ref{eq:4943050} is one of the final equations.