[tex]\Large\boxed{\begin{array}{l}\underline{\rm Demonstrac_{\!\!,}\tilde ao\,do\,teorema}\\\underline{\rm da\,energia\,cin\acute etica.}\\\sf Sabemos\,da\,equac_{\!\!,}\tilde ao\,de\,Torricelli\,que\\\sf v^2=v_0^2+2a\Delta\,s\implies \Delta\,s=\dfrac{v^2-v_0^2}{2a}\\\sf Da\,2^a\,Lei\,de\,Newton\,temos:\\\sf F_r=m\cdot a\\\sf Da\,equac_{\!\!,}\tilde ao\,do\,trabalho\,temos\\\sf T=F_r\cdot\Delta\,s\\\sf substituindo\,temos:\end{array}}[/tex]
[tex]\Large\boxed{\begin{array}{l}\sf T=m\cdot \backslash\!\!\!a\cdot\bigg(\dfrac{v^2-v_0^2}{2\backslash\!\!\!a}\bigg)\\\\\sf T=\dfrac{mv^2-mv_0^2}{2}\\\sf separando~temos\\\sf T=\dfrac{1}{2}\cdot m\cdot v^2-\dfrac{1}{2}\cdot m\cdot v_o^2\\\\\sf mas\,\dfrac{1}{2}\cdot m\cdot v^2=E_c\\\sf e\\\sf \dfrac{1}{2}\cdot m\cdot v_0^2=E_{c_0}\\\sf substituindo\,temos:\\\sf T=E_c-E_{c_0}\\\sf por\acute em\,E_c-E_{c_0}=\Delta\,E_c\\\sf ou\,seja\\\sf T=\Delta\!\,E_c\end{array}}\\[/tex]
[tex]\Large\boxed{\begin{array}{l}\sf Isto\,\acute e, o\,trabalho\,\acute e\,igual\\\sf a\,variac_{\!\!,}\tilde ao\,da\,energia\,cin\acute etica\\\huge\boxed{\boxed{\boxed{\boxed{\sf\red{\maltese}\blue{~alternativa~b}}}}}\end{array}}[/tex]
