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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Answer 1

Explanation:

Now this is a case of uniformly accelerated linear motion . Here all the equations of motion can be safely applied. In this particular case we should apply first equation of motion which says v = u + at or t = v _ u / a where u stands for initial velocity ( of the aircraft) , v stands for final velocity attained by the aircraft and a is the acceleration of the aircraft and t is the time needed by the aircraft to attain the final velocity from initial velocity travelling under uniformly accelerated motion .

In this case , u = 600 km / h , v = 1100 km / h and a = 10 km / h / s. Here we can directly put these data in the first equation of motion to arrive at the result ( no need to convert the velocities and acceleration to km / s to m / s ) .

Now , t = 1100 _ 600 / 10 = 500 / 10 or 50 s. Therefore the air craft will attain the final velocity or reach the speed barrier in 50 seconds .

Such types of air crafts which can attain or break the sound barrier are called supersonics.