posted by Harold on .
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?
I say half as much?
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