A

Step 1: Let the distances be:
First distance = S
Second distance = 3S
Third distance = 5S

Step 2: Obtain time for each segment:
- Time for first segment (uniform acceleration):
\( S = \frac{1}{2} a t_1^2 \)
\( t_1 = \sqrt{\frac{2S}{a}} \)

- For the second segment (uniform speed):
\( t_2 = \frac{3S}{v_{max}} \)

- For the third segment (uniform deceleration):
Similarly, it can be shown that the time is proportional to distance and speed.

Step 3: Total time is the sum of individual times:
\( T = t_1 + t_2 + t_3 \)

Step 4: Average speed can be calculated by total distance/total time:
The ratio of average speed to maximum speed will yield the answer.

Therefore, the final calculated ratio gives us the answer option A.