This follows directly from the definition for average acceleration:
[tex]a_{\rm ave}=\dfrac{\Delta v}{\Delta t}=\dfrac{v_f-v_i}t[/tex]
Under constant acceleration, acceleration and average acceleration are interchangeable. So we have
[tex]0.69\dfrac{\rm m}{\mathrm s^2}=\dfrac{v_f-3.5\frac{\rm m}{\rm s}}{8.3\,\mathrm s}[/tex]
[tex]\implies v_f=3.5\dfrac{\rm m}{\rm s}+\left(0.69\dfrac{\rm m}{\mathrm s^2}\right)(8.3\,\mathrm s)[/tex]
[tex]\implies\boxed{v_f=9.227\dfrac{\rm m}{\rm s}}[/tex]
