1. d. The particle starts with positive x and moves to negative x.

2. c. The velocity is the slope of the position graph. The slope is positive and constant until the position graph crosses the axis, then positive but decreasing, and finally zero when the position graph is horizontal.

3. b. A constant positive vx corresponds to a linearly increasing x, starting from $x_{\text{i}}=-10\text{m}$. The constant negative vx then corresponds to a linearly decreasing x.

4. a and b. The velocity is constant while $a=0\text{;}$ it decreases linearly while a is negative. Graphs a, b, and c all have the same acceleration, but only graphs a and b have a positive initial velocity that represents a particle moving to the right.

5. d. The acceleration vector points downhill (negative s-direction) and has the constant value $-g\text{sin}\theta$ throughout the motion.

6. c. Acceleration is the slope of the graph. The slope is zero at 2. Although the graph is steepest at 1, the slope at that point is negative, and so $a_1<a_2$. Only 3 has a positive slope, so $a_3<a_2$.

1.

1. 48 mph

2. 50 mph

3.

1. Beth

2. 20 min

5.

• a.

  

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• b. None

7. $t=6\text{s, }t=10\text{s}$

9.

11. Speeding up: $16\text{m}\text{/}{\text{s}}^2\text{;}$ slowing down: $-5.3{\text{m/s}}^2$

13.

1. $2.7{\text{m/s}}^2$

2. 2.0 m/s

3. $-2.0{\text{m/s}}^2$

15.

1. $v_{\text{max}}/t_{\text{push}}$

2. ${\displaystyle \frac{1}{2}}{v}_{\text{max}}{t}_{\text{push}}$

3. $0.95{\text{m/s}}^2$

4. $4.7\times {10}^{14}\text{m}$

17. $2.8{\text{m/s}}^2$

19.

1. $11{\text{m/s}}^2$

2. 34 m

21.

1. 24 m/s

2. 4.5 s

23. 70 m/s

25. 73 m

27.

1. 64 m

2. 7.1 s

29. 6.7 m/s

31. 16 m/s

33.

1. 21 m

2. 26 m/s

3. $24{\text{m/s}}^2$

35.

1. 2.0 s

2. $-2.0\text{m}$

37.

1. $-10\text{m}\text{/}\text{s}$

2. $-20\text{m}\text{/}\text{s}$

3. 95 m/s

39.

1. 2s, 5s

2. $-3{\text{m/s}}^2\text{,}3\text{m}\text{/}{\text{s}}^2$

41.

1. 20 s

2. 667 m

43.

45.

47. $-2\text{m}\text{/}\text{s}$

49.

1. 5 m

2. 22 m/s

51. 216 m

53.

1. $d=v_0{T}_{\text{react}}+{\displaystyle \frac{1}{2}}{\displaystyle \frac{v^2{}_0}{a}}$

2. 100 m

55. $27{\text{m/s}}^2$

57. 19.7 m

59. 29 m

61.

• a. 2.0 h

• b. 73 m

• c.

  

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63. $v_{\text{f}}=\sqrt{2gh}$

65. 0.82 m

67. 14 m/s

69.

1. 2.3 s

2. 1.2g

71. $7.5\text{m}\text{/}{\text{s}}^2$

73.

2. 25 mph, 50 mph

3. $2.7\text{m}\text{/}{\text{s}}^2\text{,}1.2\text{m}\text{/}{\text{s}}^2$

75.

3. $8\text{m}\text{/}{\text{s}}^2$

77.

3. 7.3 m

79. 3.2 m

81.

3. 45 s

83. 12.5 m/s

85. $4500\text{m}\text{/}{\text{s}}^2$