Average acceleration [tex]\bar a[/tex] given initial and final velocities [tex]v_i[/tex] and [tex]v_f[/tex], respectively, over a time interval lasting [tex]t[/tex] is
[tex]\bar a=\dfrac{v_f-v_i}t[/tex]
from which we find
[tex]t=\dfrac{v_f-v_i}{\bar a}[/tex]
To arrive at a complete stop, the cyclist's final velocity will be 0 m/s, so the time it takes to do so is
[tex]t=\dfrac{-6.5\,\frac{\mathrm m}{\mathrm s}}{-1.2\,\frac{\mathrm m}{\mathrm s^2}}=5.4\,\mathrm s[/tex]
