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A ball is bouncing elastically with a speed 1 m/s between walls of a railway compartment of size 10 m in a direction perpendicular to walls. The train is

moving at a constant velocity of 10 m/s parallel to the direction of motion of the ball. As seen from the ground,
(a) the direction of motion of the ball changes every 10 seconds.
(b) speed of ball changes every 10 seconds.
(c) average speed of ball over any 20 second interval is fixed.
(d) the acceleration of ball is the same as from the train.



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A) The direction of motion of the ball changes every 10 seconds  = correct

b)   speed of the ball changes evrey 10 seconds:  11 m/s  to 9 m/s to 11 m/s...
           9 m/s  in the direction opposite to the speed of the train.

c)  average speed:  (11*10+9*10) / 20 = 10 m/sec 
           this remains a constant for every 20 sec

d)  acceleration of the ball = 0  and acceleration of train = 0
     the acceleration is 0 whether from the train or from the ground, except when the ball bounces at the walls.

acceleration from the ground:
   when the ball bounces at the forward wall:
      velocity changes from 11 m/s to -9 m/sec.  So  - 20 / T  m/sec/sec
           where T = time duration of the collision of the ball with the wall.
      velocity changes from - 9 m/sec to 11 m/sec:  so 20/T  m/sec/sec

acceleration as seen from the train:
    at the forward wall:    1 m/s to -1 m/s  :  - 2/T   m/sec/sec
   at the rear wall:      -1 m/s  to 1 m/s  :      2 /T  m/sec/sec

So the accelerations are different during the collisions.  But in between the collisions, the ball travels with uniform speed, so acceleration is 0.  from both reference frames.

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