The distance covered by an accelerating object starting from rest is
D = (1/2 of acceleration) x (time²).
In this question,
D = 100 m
time = 3.8 s
100 = (1/2 acceleration) x (3.8s²)
100 = (1/2 a) x (14.44)
100/14.44 = 1/2 a
200/14.44 = a
a = 13.85 m/s²