Just consider that one space ship A is moving in space, far away from astrological bodies. It's engine is shut down then definitely

it is in inertial state of motion. This inertial state is consider as state 1.

Another space ship B is moving in parallel direction with A space ship with constant velocity 4 m/s with relative to A & its engine

is also shut down. This inertial state is consider as state 2.

Another space ship C is moving in parallel direction with A space ship with constant velocity 8 m/s with relative to A & its engine

is also shut down. This inertial state is consider as state 3.

Now, as physics is same in all inertial reference frame, So if rocket of 10 kg is released & fired from space ship A with

velocity 4 m/s in same direction. It will consume 0.5x m x v^2 = 80 joule of energy.

Similarly, rocket of 10 kg is fired from spaceship B with velocity 4 m/s. It will consume 0.5x m x v^2 = 80 joule of energy.

But, rocket is released & fired from space ship A with velocity 8 m/s then it will consume 0.5x m x v^2 = 320 joule of energy.

This physics clearly shows that 10 kg mass rocket require 80 joule of energy to change the state of motion from state 1 to 2

& 2 to 3. So, total energy require to change the state of motion from state 1 to 3 in steps is 80 + 80 =160 joule. ---(1)

but to change the state of motion 1 to 3 directly, rocket will consume 0.5x m x v^2 = 320 joule of energy. -----(2)

(1) & (2) are different.

why?

Because you still didn't do the equation correctly in one of the states due to the fact it is not 80 + 80 but rather 80 + 240 you forgot to add the increase in energy requirements as it is V^{2 } and not V while still taking E and not ΔE, as I said you have no idea what you are talking about and are high on that crack again. __ Do the equation correctly and you will get the correct answer!__ Stop solving it as a linear and not exponential. You cannot just take (1/2)MV

_{AB}

^{2}+ (1/2) MV

_{AB}

^{2 }, you must take (1/2)MV

_{AC}

^{2 }- (1/2) MV

_{AB}

^{2 }= ΔE

_{BC}

_{}

**Edited by VictorMedvil, 06 July 2019 - 03:58 PM.**