Question

What is the power of an airplane of mass 3000kg if when on runway it is capable of reaching speed of 80 m per second from rest in time 4 seconds?

Answer 1

It the plane is capable of reaching speed of 80 m per second from rest in time 4 seconds, then it's acceleration is:

$$a = \dfrac{80m/s-0m/s}{4s} = 20m/s^2$$

Thus, the acceleration force of the engine is:

$$F = ma = 3000\cdot 20 = 60000N = 60\times 10^3N$$

During this time the plane covers the following distance:

$$s = \dfrac{at^2}{2} = \dfrac{20\cdot 4^2}{2} = 160m$$

The work done by the engine is the following:

$$A = F\cdot s = 60\times 10^3\cdot 160 = 9.6\times 10^6J$$

Then its power:

$$P = \dfrac{A}{t} = \dfrac{ 9.6\times 10^6J}{4s} = 2.4\times 10^6W$$

Answer. $2.4\times 10^6W$.