ACCELERATING A SPACESHIP TO 1/100 SPEED OF LIGHT
Science Fiction movies show spaceships cruising at some fraction of the speed of light with the passengers in suspended animation. They land on some distant star system in a few centuries and all is well. Hmm. At .01c (1/100 the speed of light) it would take 100 years to go a single light year, and 400 years to go 4 light-years, which is the distance to Alpha Centauri, the nearest star system to earth. It is what it is, so let's see how much energy it takes to bring just a 1000kg object to .01c. Remember that a real spaceship with passengers would weigh millions of kg.
So a 1000kg object is about the same weight as a Fiat500 - with no passengers. So we're going to get this beauty up to .01c or 3x106 m/sec.
After accelerating, the final velocity will be
v = .01c = 3x106 m/sec.
Acceleration will be at 1G, which will create an earth-like gravity environment for the poor schmoes on this trip. Acceleration at 1G = 9.8 m/sec2, so:
a = 9.8 m/sec2.
Now for some high-school physics formulas:
velocity at constant acceleration = acceleration * time, or v = at.
Rearranging, t = v/a.
Distance traveled d = 1/2at2.
Substituting, d = 1/2a*(v/a)2 = 1/2v2/a.
Work (or Energy) is defined as Force x distance moved and Force = mass x acceleration, according to Sir Isaac. So:
E = F*d = m * a * d = m * a * 1/2v2/a = 1/2mv2.
This is the familiar kinetic energy equation that we all remember.
So let's plug in some values:
To get a Fiat 500 to .01C:
E = 1/2 * 1000 * (3x106)2 = 4.5x1015 joules = 4.5EJ (ekajoules)
t = 3x106/9.8 = 306,122.4 seconds = 3.54 days
To get a Fiat 500 to .1c:
E = 1/2 * 1000 * (3x107)2 = 4.5x1017 joules = 450EJ
t = 3x107/9.8 = 3,061,224 seconds = 35.4 days
Just for context, the energy production for the entire world in 2019 was 619EJ (mostly from fossil fuels). This is equivalent to 1.7EJ/day.
So, to get our Fiat to .01c would take 3.5 days and use approximately the entire world's energy production for those 3.5 days.
To get our Fiat to .1c would take 35 days, and would require the entire world's 9 month energy production.
To get a passenger ship weighing millions of tons to either of those speeds would require hundreds of times the world's yearly energy production. Probably will need to improve the technology before any of that is possible.