Irodov Problem 1.367

This problem is an extension of 1.366 and essentially asks, how long did the rocket travel according to an observer in the rocket. As the rocket accelerates and moves faster, time gets progressively slower. Let t' be the time in the reference frame of the rocket. We know that,

Irodov Problem 1.366

This problem can be considered as an extension of the problem 1.365(a). We have to simply replace V=v, to obtain the relationship between w' and the acceleration of the rocket w as seen from Earth. This is because at each instant, the moving reference frame K' has the velocity v same as that of the rocket as seen from Earth. Thus, we have,



















The distance traveled by the body can be obtained using (2) and the velocity of the body is obtained from (1). The fraction by which the velocity differs from light speed can be obtained by computing 1-v/c.

Irodov Problem 1.365

a) Let the direction of motion of the frame K' be assigned as the x-axis. Let v', x' and t' be the instantaneous velocity, position and time of the moving body as seen by the observer in frame K'. Since, the direction of motion of the accelerating body coincides with the motion of the frame K' , x -axis and x' axis coincide. From the relativistic transformations for velocity and time we have,








The acceleration of the body as seen from frame K' is then given by,























(b) In this problem the body moves along the y-axis while the frame K' moves along the x-axis. Thus, using relativistic transformations we have,





The acceleration of the body as seen in frame K' is then given by,