A particle is found to be at rest when seen from a frame S1 and moving with a constant velocity when seen from another frame S2. Mark out the possible options.
Both the frames are inertial.
Both the frames are non-inertial.
lets assume that frame S1 has velocity v and acceleration a.
Then particle P will also have velocity v and acceleration a
As P is at rest with respect to S1
VPS2=VP−VS2=V−V=0
aPS2=aP−aS2=a−a=0
Now it's mentioned that the particle P has a constant velocity with respect to S2 (frame 2)
⇒VPS2 = VP−VS2
= V - 2v
= - V
aPS2=0 (since constant velocity)
=aP−aS2=0
⇒a−aS2=0
⇒aS2=a
This proves that both the frames have same acceleration so if aS1=0
⇒aS2=0
So both are inertial
but if aS1=a then aS2=a so both will be non- inertial.
What you should understand is that given such a scenario, either both the frames are non-inertial or both the frames are inertial. One can't be inertial if the other is non-inertial.