We can solve this problem using the equation:
v_f = v_i + a*t
where v_f is the final velocity, v_i is the initial velocity, a is the acceleration, and t is the time it takes to achieve the change in speed.
Given:
v_i = 1.1 m/s
v_f = 1.5 m/s
a = 0.1 m/s²
Substituting the values into the equation, we get:
1.5 m/s = 1.1 m/s + 0.1 m/s² * t
Simplifying the equation, we get:
0.4 m/s = 0.1 m/s² * t
Dividing both sides by 0.1 m/s², we get:
t = 4 seconds
Therefore, it took the swimmer 4 seconds to achieve the change in speed from 1.1 m/s to 1.5 m/s.