The Solution:
Given:
Required:
find when the object returned to its original position.
Substitute S(t) = 0 and solve for t.
[tex]t^{\frac{5}{2}}(7-t)=0[/tex]
By factor,
[tex]\begin{gathered} t^{\frac{5}{2}}=0 \\ \\ 7-t=0 \\ t=7\text{ seconds} \end{gathered}[/tex]
Thus, the object returns to its original position after 7 seconds.
