From wikipedia:
Kinetic energy of rigid bodies
In
classical mechanics, the kinetic energy of a "point object" (a body so small that its size can be ignored), or a non-rotating
rigid body, is given by the equation
where
m is the mass and
v is the speed of the body. In
SI units (used for most modern scientific work), mass is measured in
kilograms, speed in
metres per
second, and the resulting kinetic energy is in
joules.
For example, one would calculate the kinetic energy of an 80 kg mass traveling at 18 meters per second (40 mph) as
Note that the kinetic energy increases with the square of the speed. This means, for example, that an object traveling twice as fast will have four times as much kinetic energy. As a result of this, a car traveling twice as fast requires four times as much distance to stop (assuming a constant braking force. See
mechanical work).
So, for your example converted to kilograms and meters per second:
250 knots = 128.61 meters per second
300 knots = 154.33 meters per second
85,000 = 38555.35 kilograms
Ke for the 250 knot scenario is 318863002.15 joules
Ke for the 300 knot scenario is 459150822.53 joules
So for the 20% increase in speed, Ke increased about 44% which is not 40% probably due to rounding errors. ...or maybe it's the beer...