Remember your kinematic equations for constant acceleration. One of the equations is [tex] x_{f} = x_{i} + v_{i}(t) + \frac{1}{2} at^{2} [/tex], where [tex]x_{f} [/tex] = final position, [tex]x_{i} [/tex] = initial position, [tex]v_{i}[/tex] = initial velocity, t = time, and a = acceleration.
Your initial position is where you initially were before you braked. That means [tex]x_{i} [/tex] = 100m. You final position is where you ended up after t seconds passed, so [tex]x_{f} [/tex] = 350m. The time it took you to go from 100m to 350m was t = 8.3s. You initial velocity at the initial position before you braked was [tex]v_{i}[/tex] = 60.0 m/s. Knowing these values, plug them into the equation and solve for a, your acceleration:
[tex]350\:m = 100\:m + (60.0\:m/s)(8.3\:s) + \frac{1}{2} a(8.3\:s)^{2}\\
250\:m = (60.0\:m/s)(8.3\:s) + \frac{1}{2} a(8.3\:s)^{2}\\
250\:m = 498\:m +34.445\:s^{2}(a)\\
-248\:m = 34.445\:s^{2}(a)\\
a \approx -7.2 \: m/s^{2} [/tex]
Your acceleration is approximately [tex]-7.2 \: m/s^{2} [/tex].
