Reference frames S and S′ each use an x–axis that is parallel and oriented in the…
PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials
Problem
Reference frames S and S′ each use an x–axis that is parallel and oriented in the same positive direction. Frame S′ moves with a constant velocity u in the +x–direction relative to frame S. At time t=0, the origins of the two frames coincide. An object moves only along the x–axis, and its position as a function of time in frame S is denoted x(t). The position recorded by an observer in frame S′ is x′(t). Assume all motions occur in one dimension and that both reference frames are inertial.
(a) Express the velocity v′(t) of the object measured in frame S′ in terms of the velocity v(t) measured in frame S and the relative speed u.
(b) Using appropriate time–derivative relationships, determine whether the acceleration measured in frame S′ is the same as, or different from, the acceleration measured in frame S. Provide a clear explanation of your reasoning in words and symbols.