Answer
A function expresses an object’s position, $s\left( t \right)$ , in terms of time $t$. The average velocity of the object from ${{t}_{1}}=3\text{ seconds to }{{t}_{2}}=6\text{ seconds}$ is $\frac{\Delta s}{\Delta t}=$ $\frac{s\left( 6 \right)-s\left( 3 \right)}{6-3}$.”
Work Step by Step
The average rate of change of $f$ is given as;
$\frac{\Delta y}{\Delta x}=\frac{f\left( {{x}_{2}} \right)-f\left( {{x}_{1}} \right)}{\left( {{x}_{2}}-{{x}_{1}} \right)}$
The mathematical symbol$\frac{\Delta y}{\Delta x}$ represents the change in y divided by the change in $x$.
For example, consider the function $s\left( t \right)$ at ${{t}_{1}}=3\text{ seconds to }{{t}_{2}}=6\text{ seconds}$.
The rate of change is calculated by the substitution of the value as ${{t}_{1}}=3\text{ seconds to }{{t}_{2}}=6\text{ seconds}$ and $s\left( {{t}_{1}} \right)=s\left( 3 \right)\text{ and }s\left( {{t}_{2}} \right)=s\left( 6 \right)$.
$\begin{align}
& \frac{\Delta s}{\Delta t}=\frac{s\left( {{t}_{2}} \right)-s\left( {{t}_{1}} \right)}{{{t}_{2}}-{{t}_{1}}} \\
& =\frac{s\left( 6 \right)-s\left( 3 \right)}{6-3}
\end{align}$
The average velocity of the object from ${{t}_{1}}=3\text{ seconds to }{{t}_{2}}=6\text{ seconds}$ is $\frac{\Delta s}{\Delta t}=\frac{s\left( 6 \right)-s\left( 3 \right)}{6-3}$.
