Answer:
C) [tex]\frac{5}{8}[/tex] m/s
Step-by-step explanation:
[tex]s(t)=\sqrt{1+5t}[/tex]
[tex]v(t)=\frac{d[s(t)]}{dt}[/tex]
[tex]v(t)=\frac{d(\sqrt{1+5t})}{dt}[/tex]
[tex]v(t)=\frac{5}{2\sqrt{1+5t}}[/tex]
[tex]v(3)=\frac{5}{2\sqrt{1+5(3)}}[/tex]
[tex]v(3)=\frac{5}{2\sqrt{1+15}}[/tex]
[tex]v(3)=\frac{5}{2\sqrt{16}}[/tex]
[tex]v(3)=\frac{5}{2(4)}}[/tex]
[tex]v(3)=\frac{5}{8}[/tex]
Therefore, the particle's velocity after 3 seconds is [tex]\frac{5}{8}[/tex] m/s.
