Question

An aircraft travelling at 600 km/h accelerates steadily
at 10km/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'?​

Answer 1

Answer: 50.14 s

Explanation:

We can solve this problem by the following equation:

$V=V_{o}+at$ (1)

Where:

$V=1100\frac{km}{h} \frac{1000 m}{1 km} \frac{1 h}{3600 s}=305.55 m/s$ is the final velocity of the aircraft.

$V_{o}=600\frac{km}{h} \frac{1000 m}{1 km} \frac{1 h}{3600 s}=166.66 m/s$ is the initial velocity of the aircraft

$a=2.77 m/s^{2}$ is the acceleration of the aircraft (taking into account 10 km/h=2.77 m/s and acceleration is \frac{2.77 m/s}{1 s})

$t$ is the time it takes to the aircraft to reach the sound barrier

Isolating $t$ from (1):

$t=\frac{V-V_{o}}{a}$ (2)

$t=\frac{305.55 m/s-166.66 m/s}{2.77 m/s^{2}}$ (3)

Finally:

$t=50.14 s$ (4)