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Question
An aircraft travelling at 600 km/h accelerates steadily at 10 km/h per second. Taking the speed of sound as 1100 km/h at the aircraft’s altitude, how long will it take to reach the ‘sound barrier’ ?
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Solution
Final velocity, v = 1100 km/h = 1100 × 5/18 = 305.55 m/s
Initial velocity, u = 600 km/h = 600 × 5/18 = 166.66 m/s
Acceleration = 10 km/h per second = 10 × 5/18 = 2.77 m/s2
Time taken by body,
v = u + at
t = (v - u)/a
t = (305.55 -166.66 )/2.77
t = 50.14 sec
t ≃ 50 sec
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