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Relativistic motion under a constant force from rest

Under a constant force

F

with

p (0) = 0

, momentum is

p = Ft

and

v (t) = \frac{Ft / m}{1 + ∣ F ∣ ^{2} t ^{2} / ( m ^{2} c ^{2} )} .

The speed approaches

c

without reaching it at finite time.

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