Question

The accelerations of a particle as seen from two frames $S_1$ and $S_2$ have equal magnitude $4m/s^2$

• A. the frames must be at rest with respect to each other
• B. the frames may be moving with respect to each other but neither should be acceleration with respect to the other
• C. the acceleration of $S_2$ with respect to $S_1$ may either be zero or $8m/s^2$
• D. the acceleration of $S_2$ with respect to $S_1$ may be anything between zero and $8m/s^2$

Answer 1

The correct option is D the acceleration of $S_2$ with respect to $S_1$ may be anything between zero and $8m/s^2$

The acceleration of the particle is $4m/s^2$ with respect to two frames $S_1$ and $S_2$, this means the acceleration of frame $S_1$ is $4m/s^2$ with respect to the frame of reference that is attached to the particle and same acceleration will be for the frame $S_2$.

So, the acceleration of frame $S_2$ with respect to frame $S_1$ may be from zero to $8m/s^2$ and this will depend on the direction of motion of both frames.