Consider two inertial reference frames S and S' in standard orientation so that S' moves along the positive x-axis with constant velocity u relative to S. A particle moves relative to frame S along the x-axis with instantaneous velocity Vx and instantaneous acceleration ax.
(a) Show that the instantaneous acceleration a's of the particle in frame S' is 2 3/2 и, a' =a 1- 1
(b) The proper acceleration a of a particle at a given point P on its world line is defined to be the acceleration of the particle relative to a co-moving inertial frame at P. By definition, the instantaneous velocity of the particle is zero relative to the co-moving frame. As the velocity of the particle changes along the world line, we can imagine there exist different co-moving inertial frames at different points along the world line of the particle. Now suppose u is the instantaneous velocity of the particle measured by a fixed laboratory inertial frame S. Derive the instantaneous acceleration ax of the particle frame S in terms of a and u.
(c) In
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