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

Step-by-step explanation:

We can solve this problem by the following equation:

`V=V_(o)+at` (1)

Where:

`V=1100(km)/(h) (1000 m)/(1 km) (1 h)/(3600 s)=305.55 m/s` is the final velocity of the aircraft.

`V_(o)=600(km)/(h) (1000 m)/(1 km) (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=(V-V_(o))/(a)` (2)

`t=(305.55 m/s-166.66 m/s)/(2.77 m/s^(2))` (3)

Finally:

`t=50.14 s` (4)