Hi JD-EE,
Kinetic energy is 1/2 mV^2. Potential energy is mgh. So the mass washes out of the equation. So a 3000' climb would give "gh" = 1/2 v^2 = 96000 ft^2/s^2 equals about a 438 '/s velocity change or about 300 MPH.
is correct - but it ignores the total starting energy.
They were Initially flying at M.8 (about 480 kts TAS (Vi)) at FL 350 (h1).
Shortly Afterwards they were at FL 375 (h2) with a new TAS Va
I/2 (M Vi^2) + Mgh1 = 1/2 (M Va^2) + Mg h2.
If you do the maths Va = 368 kts TAS.
The reduction from 480 to 368 kts (112 kts) was converted into an Altitude gain of 2,500ft.
From time 2.10.05 at FL 350 they had an IAS of 275 kts, so would have finished at FL 375 with an IAS of about 211 kts. (275*368/480) .