The acc. of particle as seen from 2 reference frames S1 and S2 have equal magnitude 4 m/s^2. a) the frames must be at rest w.r.t each other. b) the frame may be moving w.r.t each other. c) the acc. of S2 w.r.t S1 may either be zero or 8 m/s^2. d) the acc. of S2 w.r.t S1 may be anything between zero and 8m/s^2. Justify your ANSWERS

Since the acc. of particle as seen from 2 reference frames S1 and S2 have equal magnitude 4 m/s^2.

the answer is

a) the frames must be at rest w.r.t each other.

consider 2 trains moving in same direction with same acc. and 2 persons sitting in each of the trains are looking at a bus which is moving in same/opposite direction with different acc. as that of 2 trains,

for these 2 persons sitting in 2 diff. trains the acc. of bus running will be same as these 2 persons are at rest with respect ro each other

the answer must be d .

the angle between the accelerations of the two frames of references can vary between 0 degree to 180 degree which makes it possible that the acc of S2 wrt S1 may be anything between zero and 8m/s^2.

zero degree results in zero relative and 180 degree results in 8m/s^2 acc ,these are the max and minimum possible relative acc between the two frames given that acc of particle wrt tpo frames is 4.