1. a, c, and f. These move at constant velocity, or very nearly so. The others are accelerating.

2. a. $u\prime =u-v=-10\text{m/s}-6\text{m/s}=-16\text{m}\text{/}\text{s}$. The speed is 16 m/s.

3. c. Even the light has a slight travel time. The event is the hammer hitting the nail, not your seeing the hammer hit the nail.

4. At the same time. Mark is halfway between the tree and the pole, so the fact that he sees the lightning bolts at the same time means they happened at the same time. It’s true that Nancy sees event 1 before event 2, but the events actually occurred before she sees them. Mark and Nancy share a reference frame, because they are at rest relative to each other, and all experimenters in a reference frame, after correcting for any signal delays, agree on the spacetime coordinates of an event.

5. After. This is the same as the case of Priya and Ryan. In Mark’s reference frame, as in Ryan’s, the events are simultaneous. Nancy sees event 1 first, but the time when an event is seen is not when the event actually happens. Because all experimenters in a reference frame agree on the spacetime coordinates of an event, Nancy’s position in her reference frame cannot affect the order of the events. If Nancy had been passing Mark at the instant the lightning strikes occur in Mark’s frame, then Nancy would be equivalent to Priya. Event 2, like the firecracker at the front of Priya’s railroad car, occurs first in Nancy’s reference frame.

6. c. Nick measures proper time because Nick’s clock is present at both the “nose passes Nick” event and the “tail passes Nick” event. Proper time is the smallest measured time interval between two events.

7. $L{}_A>L{}_B=L{}_C$. Anjay measures the pole’s proper length because it is at rest in his reference frame. Proper length is the longest measured length. Beth and Charles may see the pole differently, but they share the same reference frame and their measurements of the length agree.

8. c. The rest energy $E_0$ is an invariant, the same in all inertial reference frames. Thus $m=E_0/c^2$ is independent of speed.

1. $-5.0\text{m,}1.0\text{s}\text{;}-5.0\text{m,}5.0\text{s}$

3.

1. 13 m/s

2. 3.0 m/s

3. 9.4 m/s

5. $3.0\times {10}^8\text{m}\text{/}\text{s}$

7. 167 ns

9. $1.0\mu \text{s}\text{,}2.0\mu \text{s}$

11. Simultaneously

13.

1. 5.0 y

2. 2.2 y

3. 9.0 y

15. $0.866c$

17. $46\text{ m}/\text{s}$

19.

1. Aged less

2. 14 ns

21. $0.6c$

23. $4600{\text{kg/m}}^3$

25. $3.0\times {10}^6\text{m}\text{/}\text{s}$

27.

1. $1200\text{m, }-2.0\mu \text{s}$

2. $2800\text{m,}8.7\mu \text{s}$

29. $0.71c$

31. $0.9944c$

33. $0.80c$

35. $240,000,000\text{ m}/\text{s}$

37.

1. $1.8\times {10}^{16}\text{J}$

2. $9.0\times {10}^9$

39. $0.943c$

41. 2400

43. 11.2 h

45.

1. $12.8\mu \text{s}$

2. $0.625c$

47.

1. $0.80c$

2. 16 y

49. 14 m

51.

1. $t_{\text{ D}}^{\prime }=t_{\text{ D}}^{″}=t_{\text{ D}}^{″\prime }=0\text{y},t_{\text{ E}}^{\prime }=0.42\text{y,}{t}_{\text{ E}}^{″}=0\text{y},t_{\text{ E}}^{″\prime }=-0.56\text{y}$

2. Yes, spaceship 2

3. Yes, spaceship 3

4. No

53.

1. 8.5 ly, 17 y

2. 7.4 ly, 15 y

3. Both

55. 22 m

57. $3.1\times {10}^6\text{V}$

59.

1. $0.980c$

2. $8.5\times {10}^{-11}\text{J}$

63.

1. $3.84\times {10}^8\text{m,}1.29\text{s,}5.47\times {10}^7\text{m}$

2. 0.00 m, 0.182 s, $5.47\times {10}^7\text{m}$

3. $3.84\times {10}^8\text{m,}1.28\text{s,}0.00\text{m}$

65.

1. $3.5\times {10}^{-18}\text{k}\text{/}\text{g ms}\text{,}1.1\times {10}^{-9}\text{J}$

2. $1.6\times {10}^{-18}\text{k}\text{/}\text{g ms}$

67.

1. $7.6\times {10}^{16}\text{J}$

2. 0.84 kg

69.

1. $1.3\times {10}^{17}\text{kg}$

2. $6.7\times {10}^{-12}\%$

3. 15 billion years

71.

1. $4.3\times {10}^{-12}\text{J}$

2. 0.72%

73. 1.1 pm

75. $0.85c$