Answer:
The average velocity of the particle on the time interval is -2 meters per second.
Step-by-step explanation:
Let be [tex]s(t)[/tex] the position curve which is continuous on the time interval [tex][a,b][/tex]. The average velocity ([tex]\bar v[/tex]), measured in meters per second, on the time interval is represented by the following expression:
[tex]\bar v = \frac{s(b) -s(a)}{b-a}[/tex]
Where:
[tex]a[/tex], [tex]b[/tex] - Initial and final times, measured in seconds.
[tex]s(a)[/tex], [tex]s(b)[/tex] - Initial and final positions, measured in meters.
If we know that [tex]s(t) = \frac{6}{t}[/tex], [tex]a = 1\,s[/tex] and [tex]b = 3\,s[/tex], the average velocity of the particle on the time interval is:
[tex]s(a) = 6\,\frac{m}{s}[/tex]
[tex]s(b) = 2\,\frac{m}{s}[/tex]
[tex]\bar v = \frac{2\,\frac{m}{s}-6\,\frac{m}{s} }{3\,s-1\,s}[/tex]
[tex]\bar v = -2\,\frac{m}{s}[/tex]
The average velocity of the particle on the time interval is -2 meters per second.
