Question

1)um móvel com aceleração de 50m/s² no instante 3s e velocidade de 40m/s chega no instante 12s determine a velocidade final:
2) um móvel com aceleração de 10m/s² com velocidade de 16m/s e chega com velocidade de 26m/s no instante 38s qual o instante inicial: (COM A CONTA)

Answer 1

$\Large\boxed{\begin{array}{l}\underline{\rm D~\!\!efinic_{\!\!,}\tilde ao~de~acelerac_{\!\!,}\tilde ao}\\\sf a=\dfrac{v-v_0}{t-t_0}\\\sf\\\sf a\longrightarrow acelerac_{\!\!,}\tilde ao\\\sf v\longrightarrow velocidade~final\\\sf v_0\longrightarrow velocidade~inicial\\\sf t\longrightarrow instante~final\\\sf t_0\longrightarrow instante~inicial\end{array}}$

$\Large\boxed{\begin{array}{l}\rm 1)~Um~m\acute ovel~com~acelerac_{\!\!,}\tilde ao~de~50~m/s^2\\\rm no~instante~3~s~e~velocidade~de~40~m/s\\\rm chega~no~instante~12~s.\\\rm Determine~a~velocidade~final.\\\tt dados\begin{cases}\sf a=50~m/s^2\\\sf t_0=3~s\\\sf t=12~s\\\sf v_0=40~m/s\\\sf v=?\end{cases}\\\underline{\rm soluc_{\!\!,}\tilde ao:}\\\sf a=\dfrac{v-v_0}{t-t_0}\\\sf 50=\dfrac{v-40}{12-3}\\\sf 50=\dfrac{v-40}{9}\\\sf v-40=9\cdot50\\\sf v-40=450\\\sf v=450+40\\\sf v=490~m/s\end{array}}$

$\Large\boxed{\begin{array}{l}\rm 2)~Um~m\acute ovel~com~acelerac_{\!\!,}\tilde ao~de~10~m/s^2\\\rm com~velocidade~de~16~m/s\\\rm e~chega~com~velocidade~de~26~m/s\\\rm no~instante~38~s.Qual~o~instante~inicial ?\\\tt dados\begin{cases}\sf a=10~m/s^2\\\sf v_0=16~m/s\\\sf v=26~m/s\\\sf t=38~s\\\sf t_0=?\end{cases}\\\underline{\rm soluc_{\!\!,}\tilde ao:}\\\sf a=\dfrac{v-v_0}{t-t_0}\\\sf 10=\dfrac{26-16}{38-t_0}\\\sf 10=\dfrac{10}{38-t_0}\\\sf 380-10t_0=10\\\sf -10t_0=10-380 \end{array}}$

$\Large\boxed{\begin{array}{l}\sf -10t_0=-370\cdot(-1)\\\sf 10t_0=370\\\sf t_0=\dfrac{370}{10}\\\sf t_0=37~s\end{array}}$