An aircraft traveling at 800 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’?

Question

An aircraft traveling at 800 km/h accelerates steadily at 10 km/h per second. Taking the speed of sound as 1100 km/h at the aircraft&rsquo;s altitude, how long will it take to reach the &lsquo;sound barrier&rsquo;?

Philoid · Accepted Answer

Initial velocity, u = 800 km/h

Final velocity, v = 1100 km/h

Acceleration = 10 km/h/s = 3600 km/h²

From relation, v = u+at,

On rearranging the terms, we get, v - u = at

or $t=\frac{v-u}{a}$

or $t=\frac{1100-800}{3600} = \frac{300}{3600}$

or t = 50 minutes