In an attempt to reduce the extraordinarily long travel times for voyaging to distant stars, some people have suggested traveling at close to the speed of light. Suppose you wish to visit the red giant star Betelgeuse, which is 430 ly away, and that you want your 20,000 kg rocket to move so fast that you age only 20 years during the round trip. A. How fast (v) must the rocket travel relative to earth?
0.99973 c

B. How much energy is needed to accelerate the rocket to this speed?

C. How many times larger is this energy than the total energy used by the United States in the year 2000, which was roughly 1.0×1020J?

I need help with B and C. For B, I keep getting 0 which is not correct and I don't know what I am doing wrong. C relies on my answer for B, so if I get B wrong then C is wrong as well. Thanks!

gets less

i guess it’s a and b

russian is not my first language, so i'm afraid i can't write out an answer in russian, but hopefully you can find a way to do so. here's my best translation of the problem: you're given a plot of a particle's position in one-dimensional space over time, and you're asked to find either the total distance traveled by the particle after 6 seconds had elapsed, or the total displacement of the particle after 6 seconds.

if you want the total distance traveled, you would first need to determine the particle's velocity as a function of time, then integrate that over the 6-second interval. we know the position function is quadratic with roots at 0 and 6, so we have

where is unknown. because the position is parabolic, there is symmetry about the midpoint at , and we know that

so that the position function is

which means the velocity is

then the total distance traveled is

so the total distance traveled is 20 m.

on the other hand, if you want to find displacement: the particle starts at and ends at , so its displacement is 0.