4.5 Exercise 7

The coordinate axes of the reference frame $S^{'}$ remain parallel to those of $S$, as $S^{'}$ moves away from $S$ at a constant velocity $\overset{\rightarrow}{v}_{S^{'}}^{S} = \left(4.0 \hat{i} + 3.0 \hat{j} + 5.0 \hat{k}\right) \text{m} / \text{s} .$ (a) If at time t = 0 the origins coincide, what is the position of the origin $O^{'}$ in the S frame as a function of time? (b) How is particle position for $\overset{\rightarrow}{r} \left(t\right)$ and $\overset{\rightarrow}{r}^{'} \left(t\right) ,$ as measured in S and $S^{'} ,$ respectively, related? (c) What is the relationship between particle velocities $\overset{\rightarrow}{v} \left(t\right) \text{and} \overset{\rightarrow}{v}^{'} \left(t\right) ?$ (d) How are accelerations $\overset{\rightarrow}{a} (\text{t}) \text{and} \overset{\rightarrow}{a}^{'} (\text{t})$ related?