Respuesta :
The average velocity of a particle is given by:
[tex]\vec{v}=\frac{\Delta\vec{r}}{t}[/tex]To find the change in position we subtract the initial point to the final point, then we have:
[tex]\begin{gathered} \Delta\vec{r}=\langle9-(-4),-1-(-8)\rangle \\ \Delta\vec{r}=\langle13,7\rangle \end{gathered}[/tex]Now that we have the change in position we divide it by the time, then:
[tex]\vec{v}=\frac{\Delta\vec{r}}{t}=\frac{1}{30}\langle13,7\rangle=\langle\frac{13}{30},\frac{7}{30}\rangle[/tex]Hence, the average velocity is:
[tex]\vec{v}=\langle\frac{13}{30},\frac{7}{30}\rangle[/tex]To find is magnitude we need to remember that the magnitude of any vector is given by:
[tex]v=\sqrt{v_x^2+v_y^2}[/tex]Then, in this case, we have:
[tex]\begin{gathered} v=\sqrt{(\frac{13}{30})^2+(\frac{7}{30})^2} \\ v=0.492 \end{gathered}[/tex]Therefore, the magnitude of the average velocity is 0.492 m/s
