The chemical potential energy of a certain amount of gasoline is converted into kinetic energy in a truck that increases its speed from 0 mph to 30 mph. To pass another truck the driver accelerates from 30 mph to 60 mph. Compared to the energy required to go from 0 to 30 mph, the energy required to go from 30 to 60 mph is?

Question

I say half as much?

Answer 1

use Energy = 0.5 mv^2
(this should use SI units but the conversion factors will disappear in the ratio)

at 0 the energy is 0

at 30 the energy is =0.5xmx30^2

the enrgy required to go from 0 to 30 is 0.5xmx30^2 - 0 = 0.5xmx30^2

at 60 the energy is = 0.5xmx60^2

the enrgy required to go from 30 to 60
is 0.5xmx60^2 - 0.5xmx30^2

which is 0.5xm(60^2 - 30^2)

so the ratio is

0.5xm(60^2 - 30^2)/0.5xmx30^2

= (60^2 - 30^2)/30^2

times as much