Use equation of motion:
Given: (I converted everything to meters and seconds because of acceleration in your question)
Initial velocity (u) = 600km/h = 166.6667 m/s
Final velocity (v) = 1100 km/h = 305.5556 m/s
Acceleration (a) = 10km/h every second=2.7778 m/s^2
Formula: V=U+at
305.5556=166.6667+2.7778t
2.7778t =305.5556-166.667
t = (305.5556-166.667) / (2.778) = 49.9959
time it will take to reach sound barrier = 49.9959 seconds
You can round off your answer as you wish.
