An aircraft travelling at 600km/h accelerates steadily at 10km/h second . Taking the speed of sound as 1100km/h at the aircraft's altitude , how long will it take to reach the 'sound barrier'?
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The aircraft has to cross sound barrier ,i.e.v=1100 km/h =1100 x 5/18= 2750/9 m/s
u=600 km/h = 600 x 5/18 = 1500/9 m/s
the acceleration of the aircraft is 10 km/h per second
a= 10 km/h/s = 10 x 5/18 m/s/s = 25/9 m/s^2
using first equation of motion
v = u+at
2750/9= 1500/9 + 25t/9
2750 = 1500 + 25 t
2750 - 1500 / 25 = 1250/25
= 50s
hence the aircraft will cross the sound barrier in 50 secs