Chapter 1

37. A typical sugar cube has an edge length of 1 cm. If you had a cubical box that contained a mole of sugar cubes, what would its edge length be? (One mole = 6.02 x 1023units.)

38. An  old  manuscript  reveals  that  a  landowner  in  the  time of  King  Arthur  held  3.00  acres  of  plowed  land  plus  a  livestock area of 25.0 perches by 4.00 perches. What was the total area in (a) the old unit of roods and (b) the more modern unit of square meters? Here, 1 acre is an area of 40 perches by 4 perches, 1 rood is an area of 40 perches by 1 perch, and 1 perch is  the length 16.5 ft.

39. A  tourist purchases a car in England and ships it home to the United States. The car sticker advertised that the car's fuel consumption was  at the rate of 40 miles per gallon on the open road. The  tourist does not realize  that the u.K. gallon differs  from  the U.S. gallon:
1 U.K. gallon = 4.5460900 liters
1 U.S. gallon = 3.7854118 liters.
For a trip of 750 miles (in the United States), how many gallons of fuel does (a) the mistaken tourist believe she needs and (b) the car actually require?

40. Using   conversions   and   data   in   the   chapter,   determine the  number  of  hydrogen  atoms  required  to  obtain  1.0 kg  of hydrogen. A hydrogen atom has a mass of 1.0 U.

41. A  cord is  a  volume  of cut wood  equal  to  a  stack  8 ft long, 4 ft wide, and 4 ft high. How many cords are in 1.0 m3?

42. One molecule of water (H2O) contains two atoms of hydrogen and one atom of oxygen. A hydrogen atom has a mass of 1.0 u and an atom of oxygen has a mass of 16 u, approximately.  (a)  What is the mass  in  kilograms of one molecule  of water?  (b)  How many molecules of water are in the world's oceans, which have an estimated total mass of 1.4 x 1021  kg?

43. A  person on a  diet  might lose  2.3  kg per week.  Express the mass loss rate in milligrams per second, as if the dieter could sense the second-by-second loss.

44. What mass of water fell on the town in Problem 7? Water has a density of 1.0 x 103  kg/m3.

46. A  unit  of  area  often  used  in  measuring  land  areas  is  the hectare,   defined  as  104  m2.  An  open-pit  coal   mine  consumes 75  hectares of land, down to a depth of 26 m, each year. What volume of earth, in cubic kilometers, is removed in this time?

47. An astronomical unit (AU) is the average distance between Earth and the Sun, approximately 1.50 x 108 km.  The speed of light is about 3.0 x 108 m/s. Express the speed of light in astronomical units per minute.

48. The common Eastern mole, a mammal, typically has a mass of 75 g, which corresponds to about 7.5 moles of atoms.  (A mole of atoms is  6.02 x 1023  atoms.)  In atomic mass units  (u), what is  the average mass of the atoms in the common Eastern mole?

50. You receive orders to sail due east for 24.5 mi to put your salvage ship  directly over a sunken pirate ship. However, when your divers probe the ocean floor at that location and find  no evidence of a ship, you radio back to your source of information, only to discover  that  the  sailing  distance  was  supposed  to  be  24.5  nautical miles,  not regular  miles.

Chapter 2

1. During a  hard sneeze, your eyes might shut for  0.50 s.  If you are driving a car at 90 km/h during such a sneeze, how far does the car move during that time?

2. Compute your average velocity in the following two cases: (a) You  walk  73.2 m at a speed  of 1.22 m/s  and  then  run 73.2 m  at a speed of 3.05 m/s along a straight track. (b) You walk for 1.00 min at a speed of 1.22 m/s and then run for 1.00 min at 3.05 m/s along a straight track. (c) Graph x versus t for both cases and indicate how the average velocity is found on the graph.

3. An automobile travels on a straight road for  40 km at 30 km/h.1t then continues in the same direction for another 40  km at 60  km/h. (a) What is the average velocity of the car during the full 80 km trip? (b) What is the average speed? (c) Graph x versus t and indicate how the average velocity is found on the graph.

4. A car travels up a hill at a constant speed of 40 km/h and returns down the hill at a constant speed of 60 km/h. Calculate the average speed for the round trip.

5. The position of an object moving along an x axis is given by x = 3t – 4t2 + t3, where x is in meters and t in seconds. Find the position of the object at the following values of t:  (a) 1 s, (b) 2 s, (c) 3 s, and (d) 4 s.  (e) What is the object's displacement between t = 0 and t = 4 s?  (f) What is its average velocity for the time interval from t = 2 s to t = 4 s?  (g)  Graph x versus t for 0 ? t ? 4 s and indicate how the answer for (f) can be found on the graph.

6. The  1992  world  speed  record  for  a  bicycle  (human-powered vehicle)  was  set by Chris  Huber. His  time  through  the  measured 200 m  stretch  was  a  sizzling  6.509 s,  at  which  he  commented, "Cogito ergo  zoom!" (I think, therefore  I go  fast!).  In 2001, Sam Whittingham   beat   Huber's   record   by   19.0 km/h.   What   was Whittingham's time through the 200 m?

7. Two  trains,  each  having  a  speed  of  30 km/h,  are  headed  at each other on the same straight track. A  bird that can fly  60 km/h flies off the front of one train when they are 60 km apart and heads directly  for  the other train.  On reaching  the  other train, the  bird flies  directly back to the first  train, and so forth. (We have no idea why a bird would behave in this way.) What is the total distance the bird travels before the trains collide?

8. Figure 2-21  shows a general situation in which a stream of people attempt to escape through an exit door that  turns  out  to  be locked. The people  move  toward  the  door  at speed  Vs  =  3.50 m/s, are each d =  0.25 m in depth, and are separated by L  =  1.75 m. The arrangement in Fig. 2-21 occurs at time t = 0.  (a) At what average rate does the layer of people at the door increase? (b) At what time does the layer's depth reach 5.0m?

9. In 1 km races, runner 1 on track 1 (with time 2 min, 27.95 s)  appears  to be  faster  than runner 2 on  track 2  (2 min, 28.15 s). However, length Lz of track 2 might be slightly greater than length LI of track 1. How large can Lz -  LI be for us still to conclude that runner 1 is faster?

11. You  are  to  drive  to  an interview in  another town, at a distance of 300 km on an expressway. The interview is at 11:15 A.M. You plan to drive at 100 km/h, so you leave at 8:00 A.M. to allow some extra time. You  drive  at that speed for  the  first  100 km, but  then construction work forces  you to  slow  to 40  km/h for  40  km. What would be the least speed needed for the rest of the trip to arrive in time for the interview?

12. An abrupt slowdown  in  concentrated traffic can travel as  a pulse, termed a shock wave,  along the  line  of  cars,  either  downstream  (in  the  traffic  direction)  or  upstream,  or  it  can  be  stationary.  Figure  2-22  shows  a  uniformly spaced  line  of cars  moving  at  speed  v =  25.0 m/s  toward  a  uniformly  spaced  line  of  slow  cars  moving  at  speed  Vs  =  5.00 m/s. Assume  that  each  faster  car  adds  length  L  =  12.0 m  (car  length plus buffer zone) to the line of slow cars when it joins the line, and assume it slows abruptly at the last instant. (a) For what separation distance d between the faster cars does the shock wave remain stationary?  If the  separation is  twice  that amount, what are  the  (b) speed  and  (c)  direction  (upstream  or  downstream)  of  the  shock wave?

13. You  drive  on  Interstate  10  from  San  Antonio  to Houston, half the time at 55  km/h and the other half at 90 km/h. On the way back you  travel half the  distance  at 55  km/h  and  the other  half  at  90 km/h.  What  is  your  average  speed  (a)  from  San Antonio to Houston, (b) from Houston back to San Antonio, and ( c) for the entire trip? (d) What is your average velocity for the entire trip?  (e) Sketch x versus t for (a), assuming the motion is  all in the positive x direction. Indicate how the average velocity can be found on the sketch.

14. An electron moving along the x axis has a position given by x = 16te-t m, where t is in seconds. How far is the electron from the origin when it momentarily stops?

15. (a)  If a particle's  position is  given  by x  =  4 - 12t + 3t2 (where  t is  in  seconds  and x is  in  meters), what is  its  velocity  at t  =  1 s?  (b)  Is it moving in the positive or negative direction of x just then?  (c)  What is its  speed  just  then?  (d)  Is  the  speed increasing  or  decreasing  just  then?  (e) Is there ever an instant when the velocity is zero? If so, give the time t; if not, answer no. (f) Is there a time after t = 3 s when the particle is moving in the negative direction of x? If so, give the time t; if not, answer no.

16. The position function x(t) of a particle moving along an x axis is  x  =  4.0 -  6.0t2,  with  x  in  meters  and  t in  seconds.  (a)  At what time and (b) where does the particle (momentarily) stop? At what (c)  negative  time  and  (d)  positive  time  does  the  particle  pass through the origin? (e) Graph x versus t for the range - 5 s to + 5 s. (f) To shift the curve rightward on the graph, should we include the term  +20t or the  term  -20t in x(t)?  (g)  Does  that  inclusion  increase or decrease the value of x  at which the particle momentarily stops?

17. The position of a particle moving along the x axis is given in centimeters  by  x =  9.75 +1.50t3,  where  t  is  in seconds.  Calculate (a)  the  average  velocity  during  the  time  interval t =  2.00 s to t = 3.00 s; (b) the instantaneous velocity at t =  2.00 s; (c) the instantaneous  velocity  at  t = 3.00 s;  (d)  the  instantaneous velocity  at  t = 2.50 s; and (e) the instantaneous velocity when the particle is midway between its  positions at t = 2.00 sand t = 3.00 s.  (f)  Graph x versus t and indicate your answers graphically.

18. The position of a particle moving along an x axis is given by x = 12t2 - 2t3, where x is in meters and t is in seconds. Determine (a)  the  position,  (b)  the  velocity,  and  (c)  the  acceleration  of the particle at t =  3.0 s.  (d) What is  the maximum positive coordinate reached by the particle and (e) at what time is it reached? (f) What is the maximum positive velocity reached by the particle and (g) at what time is it reached? (h) What is the acceleration of the particle at the instant the particle is not moving (other than at t = 0)? (i)  Determine  the  average  velocity  of the  particle  between t  =  0 and t =  3 s.

19. At a  certain  time  a  particle  had  a  speed  of 18 m/s  in the positive x  direction, and 2.4 s later its speed was 30 m/s in  the opposite direction. What is the average acceleration of the particle during this 2.4 s interval?

20. (a)  If the  position  of  a  particle  is  given  by  x = 20t - 5t3, where x is  in meters and t is  in seconds, when, if ever, is  the particle's  velocity  zero?  (b)  When  is  its  acceleration  a zero?  (c)  For what time range (positive or negative) is  a negative? (d) Positive? (e) Graph x(t), v(t), and a(t).

21. From  t =  0  to  t =  5.00 min,  a  man  stands  still,  and  from t = 5.00 min to t = 10.0 min, he walks briskly in a straight line  at a constant speed  of 2.20 m/s. What  are  (a)  his  average  velocity  vavg and (b) his average acceleration  aavg  in the time interval 2.00 min to 8.00 min? What are (c) vavg  and (d)  aavg  in the time interval 3.00 min to 9.00 min?  (e) Sketch x versus t and v versus t,  and indicate how the answers to (a) through (d) can be obtained from the graphs.

22. The position of a particle moving along the x  axis  depends on the time  according to the equation x  = ct2 - bt3 ,  where x  is  in meters and t in seconds. What are the units of (a) constant e and (b) constant b?  Let their numerical values be 3.0 and 2.0, respectively. (c) At what time does the particle reach its maximum positive x position? From t =  0.0 s to t =  4.0 s, (d) what distance does the particle move and (e) what is its displacement? Find its velocity at times (f)  1.0 s,  (g)  2.0 s,  (h)  3.0 s,  and  (i)  4.0 s.  Find  its  acceleration  at times (j) 1.0 s, (k) 2.0 s, (1)  3.0 s, and (m) 4.0 s.

23. An electron with an initial velocity  Vo  =  1.50 x 105  m/s enters a region of length L  =  1.00 cm where it is  electrically accelerated  (Fig.  2-23).  It emerges  with v  = 5.70 x 106 m/s. What is its acceleration, assumed constant?

24. Catapulting   mushrooms. Certain mushrooms launch their spores by a catapult mechanism. As water condenses from the air onto a spore that is attached to the  mushroom,  a  drop  grows  on one  side  of the  spore  and  a  film grows on  the other side. The spore is bent over by the drop's weight, but when the film reaches the drop, the drop's water suddenly spreads into the film and the spore springs upward so rapidly that it is slung off into the air. Typically, the spore reaches a speed of 1.6 m/s in a 5.0 ?m launch; its speed is  then reduced to zero in 1.0 mm by the air. Using that data and assuming constant accelerations, find the acceleration in terms of g during (a) the launch and (b) the speed reduction.

25. An electric vehicle starts from rest and  accelerates at a rate of 2.0 m/s2  in a straight line until it reaches a speed of 20 m/s. The vehicle  then slows  at a constant rate  of 1.0 m/s2  until it stops.  (a) How much  time  elapses from  start to  stop?  (b)  How far  does  the vehicle travel from start to stop?

26. A  muon  (an  elementary  particle)  enters  a  region  with  a speed of 5.00 x 106  m/s  and  then  is  slowed  at  the rate of 1.25 x 1014  m/s2.   (a)  How far  does  the  muon  take  to  stop?  (b)  Graph x versus t and v versus t for the muon.

27. An electron has a constant acceleration of +3.2 m/s2. At a certain instant its velocity is +9.6 m/s. What is its velocity (a) 2.5 s earlier and (b) 2.5 s later?

28. On a dry road, a car with good tires may be able to brake with a constant deceleration of 4.92 m/s2 . (a) How long does such a car, initially traveling at 24.6 m/s, take to stop? (b) How far does it travel in this time? (c) Graph x versus t and v versus t for the deceleration.

29. A certain elevator cab has a total run of 190 m and a maximum speed  of 305 m/min,  and  it  accelerates  from  rest  and  then back to rest at 1.22 m/s2 .  (a) How far does the cab move while accelerating  to  full  speed from  rest?  (b)  How long does it take to make the nonstop 190 m run, starting and ending at rest?

30. The brakes on your car can slow you at a rate of 5.2 m/s2. (a) If you are going 137 km/h and suddenly see a state trooper, what is the  minimum  time  in  which  you  can  get  your  car  under  the  90 km/h  speed limit?  (The  answer  reveals  the  futility  of braking  to keep  your  high  speed from  being  detected  with  a  radar  or laser gun.) (b) Graph x versus t and v versus t for such a slowing.

31. Suppose a rocket ship in deep  space moves  with  constant acceleration equal to 9.8 m/s2,  which gives the illusion of normal gravity during the flight.  (a) If it starts from rest, how long will it  take to acquire a speed one-tenth that of light, which travels  at 3.0 x 108  m/s? (b) How far will it travel in so doing?

32. A world's land speed record was  set by  Colonel John P. Stapp when in March 1954 he rode a rocket-propelled sled that moved along a track at 1020 km/h. He and the sled were brought to a stop in 1.4 s. (See Fig. 2-7.) In terms of g, what acceleration did he experience while stopping?

33. A car traveling 56.0 km/h is 24.0 m from a barrier when the driver slams on the brakes. The car hits the barrier 2.00 s later. (a) What is  the magnitude of the car's constant acceleration before impact? (b) How fast is the car traveling at impact?

34. In Fig. 2-24, a red car and a green car, identical except for the color, move toward each other in adjacent lanes and parallel to an x axis. At time t = 0, the red car is at xr = 0 and the green car is at xg = 220 m. If the red car has a constant velocity of 20 km/h, the cars pass each other at x = 44.5 m, and if it has a constant velocity of 40 km/h, they pass each other at x = 76.6 m. What are (a) the initial velocity and (b) the constant acceleration of the green car?

35. Figure  2-24  shows  a  red  car and  a  green  car  that  move  toward each other. Figure 2-25 is  a graph of their motion, showing  the  positions xg0  = 270 m  and  xr0  =   -35.0 m  at time t  = 0. The green car has a constant speed of 20.0 m/s and  the  red car begins from rest. What is the acceleration magnitude of the red car?

36. A  car moves  along  an  x  axis  through  a  distance  of 900 m, starting  at  rest  (at  x  = 0)  and  ending  at  rest  (at  x  =  900 m). Through the first 1/4 of that distance, its acceleration is +2.25 m/s2. Through the rest of that distance, its acceleration is -0.750 m/s2. What  are  (a)  its  travel time  through  the  900 m and  (b)  its  maximum speed?  (c)  Graph position x, velocity v, and acceleration a versus time t for the trip.

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