Can I check if the answer for the final part is actually
By Newton's 3rd law, the force pushing the athlete forward cannot exceed the friction provided by the track (otherwise they will slip), The friction provided by the track is
Hence the maximum acceleration
For a race of 800m where the maximum speed is 8m/s, we first need to consider the time taken whilst accelerating from the standing start of 0m/s to 8m/s.
we get to
and distance covered in this time whilst accelerating:
Hence the time whilst running at constant 8m/s is given by
so (nearly there!) total time is given by: