Introduction to Classical Mechanics · Problem 12.36

4-vectors — Morin

Physics — Mechanics · force-relativistic

Problem

Pushing on a mass ** (a) A mass

m

starts at rest. You push on it with a constant force

F

. How much time

t

does it take for the mass to move a distance

x

? (Both

t

and

x

here are measured in the lab frame.) (b) After a very long time,

m

's speed will approach

c

. It turns out that it approaches

c

sufficiently fast so that after a very long time,

m

will remain (approximately) a constant distance (as measured in the lab frame) behind a photon that was emitted at

t = 0

from the starting position of

m

. What is this distance?