[panic]

Nice article, but I couldn't pass up a chance to correct Elon Musk's math:

It is important to note that the amount of energy needed to achieve a given velocity increases with the square, so going from 1000 km/h to 2000 km/h takes four times as much energy as going from 0 km/h to 1000 km/h, not twice as much.

Three times, not four--you already spent a quarter of the energy getting to 1000 km/h. Getting the rest of the way to 2000 km/h takes the remaining three quarters.

[notdonspaulding]

I believe you've misunderstood his English. If it takes 1 Joule to accelerate the mass from 0-1000km/h, it will take 4 Joules to accelerate the same mass from 0-2000km/h.

Elon is calling that four times as much as because he's considering the total energy required to accelerate from 0 in both numbers. I think you're just accounting for it differently by saying it takes 3 times as much as the original energy input to go from 1000km/h to 2000km/h.

I'm a complete physics novice, I'm open to being schooled on this if I'm completely missing both yours and Elon's concepts here.

[tim333]

I think panic is correct. "from 1000 km/h to 2000 km/h" means from 1000 km/h to 2000 km/h, not 0-2000 kph. Though presumably Elon was thinking of the latter.

[rimantas]

Read it as "going from target velocity of 1000km/h to 2000km/h".

[pbreit]

I don't think he worded it quite right but the inclusion of "not twice as much" makes it clearer that he was referring to "0 to 1,000" vs "0 to 2,000" (not 0 to 1,000 vs 1,000 to 2,000). So I believe the error was in the writing, not the math or understanding. Which he even pre-apologized for presumably in an attempt to assuage the nit-pickers.