an aircraft travelling at 600km/hr accelerates steadily at 10 km /h every second. Assuming speed of sound is 100 km /h t the aircrafts altitude , how long will it take to reach the sound barrier
I think you have garbled your values.
If the speed of sound is 100 km/hr and the plane is already going 600 km/hr ...
At any rate, when you get the speeds figured out, the number of seconds it takes is just the extra speed needed divided by 10, since the speed increases 10km/hr per second.