If "during this time" refers to the 5 second interval mentioned above, then the average acceleration is
[tex]\bar a=\dfrac{v-v_0}{t-t_0}=\dfrac{40\,\frac{\mathrm m}{\mathrm s}-10\,\frac{\mathrm m}{\mathrm s}}{5\,\mathrm s-0\,\mathrm s}[/tex]
Notice that we took the start time to be the start of the 5 second interval and set that to [tex]t_0=0[/tex]. The starting velocity [tex]v_0[/tex] is the velocity measured at the start of the interval, and [tex]v[/tex] is the velocity measured at its end.
So the average velocity over these 5 seconds is
[tex]\bar a=\dfrac{30\,\frac{\mathrm m}{\mathrm s}}{5\,\mathrm s}=6\,\dfrac{\mathrm m}{\mathrm s^2}[/tex]
