The following table gives the position $s\left(t\right)$ of an object moving along a line at time $t$. Determine the average velocities over the time intervals $\left\lbrack1,1.01\right\rbrack$, $\left\lbrack1,1.001\right\rbrack$, and $\left\lbrack1,1.0001^{}\right.]$. Then make a conjecture about the value of the instantaneous velocity at $t=1$. <IMAGE>

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1. Identify the formula for average velocity over a time interval [a, b], which is given by the change in position divided by the change in time: $v_{avg}=\frac{s(b)-s(a)}{b-a}$.
2. For the interval [1, 1.01], calculate the average velocity using the positions at t = 1 and t = 1.01. Substitute these values into the average velocity formula.
3. For the interval [1, 1.001], calculate the average velocity using the positions at t = 1 and t = 1.001. Again, substitute these values into the average velocity formula.
4. For the interval [1, 1.0001], calculate the average velocity using the positions at t = 1 and t = 1.0001. Substitute these values into the average velocity formula.
5. Observe the trend in the average velocities as the time interval decreases. Use this trend to make a conjecture about the instantaneous velocity at t = 1, which is the limit of the average velocity as the interval approaches zero.