3. The position of a particle after $t$ seconds is given by $f(t)=2^{t}$ meters. Fill in the table below with the indicated average velocities of the particle. Then, estimate the instantaneous velocity of the particle at $t=1$ second, and include the proper units with your answer. \begin{tabular}{|c||c|c|c|c|} \hline$h$ & 0.1 & 0.01 & 0.001 & 0.0001 \\ \hline$A V_{[1,1+h]}$ & & & & \\ \hline \end{tabular}

Step 1 ：The position of a particle after $t$ seconds is given by $f(t)=2^{t}$ meters. We are asked to find the average velocities over the intervals $[1, 1+h]$ for various values of $h$.

Step 2 ：The average velocity of a particle over an interval $[a, b]$ is given by the formula $\frac{f(b) - f(a)}{b - a}$. We can use this formula with the given function $f(t) = 2^t$ to calculate the average velocities.

Step 3 ：For $h$ values of 0.1, 0.01, 0.001, and 0.0001, the calculated average velocities are approximately 1.435, 1.391, 1.387, and 1.386 respectively.

Step 4 ：As $h$ gets smaller, the average velocity seems to be approaching a certain value. This value is the instantaneous velocity at $t=1$.

Step 5 ：The instantaneous velocity of the particle at $t=1$ second is approximately \(\boxed{1.386}\) meters per second.