Remark: Since the data is discrete, we are going to assume mean velocities in each time intervals, otherwise the movement's law would have to be given explicitly.
Another approach is to compute the velocity first and then the acceleration, without using equations explicitly. Since you are given five pairs $(t,d)$, where $t$ is the time and $d$ is the distance, we can evaluate the average velocity $v=\frac{\Delta d}{\Delta t}$ over each period $\left[t_{i},t_{i+1}\right] $, starting at $t=0$ s, and $\Delta t_{i}=d_{i+1}-d_{i}$. The measurements are equally spaced, with $\Delta t=1$ s. We get the following average velocities:
- $i=0\quad t\in \left[ 0,1\right] $ s,$\quad v=\frac{1-0}{1}=1$ ms$^{-1}=1 \text{m/s}$,
- $i=1\quad t\in \left[ 1,2\right] $ s,$\quad v=\frac{3-1}{1}=2$ ms$^{-1}$,
- $i=2\quad t\in \left[ 2,3\right] $ s,$\quad v=\frac{6-3}{1}=3$ ms$^{-1}$,
- $i=3\quad t\in \left[ 3,4\right] $ s,$\quad v=\frac{10-6}{1}=4$ ms$^{-1}$.
Now we compute the average acceleration from one period to the next $a=\dfrac{\Delta v}{% \Delta t}$:
- from $\left[ 0,1\right] $ to $\left[ 1,2\right] $ s,$\quad a=% \frac{2-1}{1}=1$ ms$^{-2},$
- from $\left[ 1,2\right] $ to $\left[ 2,3\right] $ s,$\quad a=% \frac{3-2}{1}=1$ ms$^{-2},$
- from $\left[ 2,3\right] $ to $\left[ 3,4\right] $ s,$\quad a=% \frac{4-3}{1}=1$ ms$^{-2}.$
Thus the average acceleration $a$ is constant: $a=1$ $\text{ms}^{-2}=1\text{m/s}^{2}$.
In summary we get the following table with data and computations:
$\begin{array}{ccccccccc} i & t_{i}\text{ (s)} & & d_{i}\text{ (m)} & & v_{i}\text{ (ms}^{-1}% \text{)} & & a_{i}\text{ (ms}^{-2}\text{)} & \\ & & & & & & & & \\ & 0 & & 0 & & & & & \\ 0 & 1 & & 1 & & 1 & & & \\ 1 & 2 & & 3 & & 2 & & 1 & \\ 2 & 3 & & 6 & & 3 & & 1 & \\ 3 & 4 & & 10 & & 4 & & 1 & \end{array}.$
Notes:
- Since the measurements are discrete, the velocity and accelerate values are mean values and not instant one.
- The acceleration unit ms$^{-2}$ (or $\text{m}/\text{s}^2$) is the same as meters/sec/sec in the question, tought this is an abuse of notation, since the meaning is (meters/second)/second.