College Physics, 6th Edition Figures Chapter 2 College Physics, 6th Edition Wilson / Buffa / Lou © 2007 Pearson Prentice Hall This work is protected by United States copyright laws and is provided solely for the use of instructors in teaching their courses and assessing student learning. Dissemination or sale of any part of this work (including on the World Wide Web) will destroy the integrity of the work and is not permitted. The work and materials from it should never be made available to students except by instructors using the accompanying text in their classes. All recipients of this work are expected to abide by these restrictions and to honor the intended pedagogical purposes and the needs of other instructors who rely on these materials.

Figure 2-1 Distance – total path length In driving to State University from Hometown, one student may take the shortest route and travel a distance of 81 km (50 mi). Another student takes a longer route in order to visit a friend in Podunk before returning to school. The longer trip is in two segments, but the distance traveled is the total length, 97 km + 48 km = 145 km (90 mi).

Figure 2-4 Distance (scalar) and displacement (vector) (a) The distance (straight-line path) between the student and the physics lab is 8.0 m and is a scalar quantity. (b) To indicate displacement, x1 and x2 specify the initial and final positions, respectively. The displacement is then Δx = x2 – x1 = 9.0 m – 1.0 m = +8.0 m — that is, 8.0 m in the positive x-direction.

Learn by Drawing 2-1 Cartesian Coordinates and One-Dimensional Displacement (a) A two-dimensional Cartesian coordinate system. A displacement vector d locates a point (x, y). (b) For one-dimensional, or straight-line, motion, it is convenient to orient one of the coordinate axes along the direction of motion.

Figure 2-6 Uniform linear motion – constant velocity In uniform linear motion, an object travels at a constant velocity, covering the same distance in equal time intervals. (a) Here, a car travels 50 km each hour. (b) An x-versus-t plot is a straight line, since equal displacements are covered in equal times. The numerical value of the slope of the line is equal to the magnitude of the velocity, and the sign of the slope gives its direction. (The average velocity equals the instantaneous velocity in this case. Why?)

Figure 2-7 Position-versus-time graph for an object in uniform motion in the negative x-direction A straight line on an x-versus-t plot with a negative slope indicates uniform motion in the negative x-direction. Note that the object’s location changes at a constant rate. At t = 4.0 h the object is at x = 0. How would the graph look if the motion continues for t > 4.0 h?

Figure 2-8 Position-versus-time graph for an object in nonuniform linear motion For a nonuniform velocity, an x-versus-t plot is a curved line. The slope of the line between two points is the average velocity between those positions, and the instantaneous velocity is the slope of a line tangent to the curve at any point. Five tangent lines are shown, with the intervals for Δx/Δt in the fifth. Can you describe the object’s motion in words?

Figure 2-9 Acceleration – the time rate of change of velocity Since velocity is a vector quantity, with magnitude and direction, an acceleration can occur when there is (a) a change in magnitude, but not direction; (b) a change in direction, but not magnitude; or (c) a change in both magnitude and direction.

Learn by Drawing 2-2 Signs of Velocity and Acceleration

Figure 2-10 Velocity-versus-time graphs for motions with constant accelerations The slope of a -versus-t plot is the acceleration. (a) A positive slope indicates an increase in the velocity in the positive direction. The vertical arrows to the right indicate how the acceleration adds velocity to the initial velocity v0. (b) A negative slope indicates a decrease in the initial velocity v0, or a deceleration. (c) Here a negative slope indicates a negative acceleration, but the initial velocity is in the negative direction, -v0, so the speed of the object increases in that direction. (d) The situation here is initially similar to that of part (b) but ends up resembling that in part (c). Can you explain what happened at time t1 ?

Figure 2-11 Away they go! Two dune buggies accelerate away from each other. How far are they apart at a later time? See Example 2.7.

Figure 2-12 Vehicle stopping distance A sketch to help visualize the situation in Example 2.8.

Figure 2-13 v-versus-t graphs, one more time (a) In the straight-line plot for a constant acceleration, the area under the curve is equal to x, the distance covered. (b) If v0 is not zero, the distance is still given by the area under the curve, here divided into two parts, areas A1 and A2 .

Figure 2-14 Free fall and air resistance (a) When dropped simultaneously from the same height, a feather falls more slowly than a coin, because of air resistance. But when both objects are dropped in an evacuated container with a good partial vacuum, where air resistance is negligible, the feather and the coin both have the same constant acceleration.

Figure 2-16 Free fall up and down Note the lengths of the velocity and acceleration vectors at different times. (The upward and downward paths of the ball are horizontally displaced for illustration purposes.) See Example 2.11.

Figure 2-17 Speed versus velocity (b) Exercise 21 21. An insect crawls along the edge of a rectangular swimming pool of length 27 m and width 21 m (Fig. 2.17). If it crawls from corner A to corner B in 30 min, (a) what is its average speed, and (b) what is the magnitude of its average velocity? (a) 2.7 cm/s (b) 1.9 cm/s

Figure 2-18 Position versus time 24. A plot of position versus time is shown in Fig. 2.18 for an object in linear motion. (a) What are the average velocities for the segments AB, BC, CD, DE, EF, FG, and BG? (b) State whether the motion is uniform or nonuniform in each case. (c) What is the instantaneous velocity at point D?   Exercise 24

Figure 2-19 Position versus time 25 Exercise 25

Figure 2-20 When and where do they meet? 30. Two runners approaching each other on a straight track have constant speeds of and respectively, when they are 100 m apart (Fig. 2.20). How long will it take for the runners to meet, and at what position will they meet if they maintain these speeds?  12.5 s, 56.3 m (relative to runner on left) Exercise 30

Figure 2-21 Description of motion Exercise 38 38. Describe the motions of the two objects that have the velocity-versus-time plots shown in Fig. 2.21.

Figure 2-22 Velocity versus time Exercises 50 and 75 50. What is the acceleration for each graph segment in Fig. 2.22? Describe the motion of the object over the total time interval.

Figure 2-23 Velocity versus time 51. Figure 2.23 shows a plot of velocity versus time for an object in linear motion. (a) Compute the acceleration for each phase of motion. (b) Describe how the object moves during the last time segment. Exercises 51 and 79

Figure 2-24 Hit the professor 104. In Fig. 2.24, a student at a window on the second floor of a dorm sees his math professor walking on the sidewalk beside the building. He drops a water balloon from 18.0 m above the ground when the professor is 1.00 m from the point directly beneath the window. If the professor is 170 cm tall and walks at a rate of does the balloon hit her? If not, how close does it come? Exercise 104 hits 14 cm in front of the professor

Figure 2-25 From where did it come? 107 It takes 0.210 s for a dropped object to pass a window that is 1.35 m tall. From what height above the top of the window was the object released? (See  Fig. 2.25.) Exercise 107 1.49 m above the top of the window

Figure 2-26 A tie race 111 A car and a motorcycle start from rest at the same time on a straight track, but the motorcycle is 25.0 m behind the car (Fig. 2.26). The car accelerates at a uniform rate of 3.70 m/s2 and the motorcycle at a uniform rate of (a) How much time elapses before the motorcycle overtakes the car? (b) How far will each have traveled during that time? (c) How far ahead of the car will the motorcycle be 2.00 s later? (Both vehicles are still accelerating.) (a) 8.45 s (b) (c) 13 m Exercise 111

Figure 2-28 Down she comes 117 Let’s investigate a possible vertical landing on Mars that includes two segments: free fall followed by a parachute deployment. Assume the probe is close to the surface, so the Martian acceleration due to gravity is constant at Suppose the lander is initially moving vertically downward at at a height of above the surface. Neglect air resistance during the free-fall phase. Assume it first free-falls for (The parachutes don’t open until it is from the surface. See Fig. 2.28.) (a) Determine the lander’s speed at the end of the 8000-m free-fall drop. (b) At above the surface, the parachute deploys and the lander immediately begins to slow. If it can survive hitting the surface at up to determine the minimum constant deceleration needed during this phase. (c) What is the total time taken to land from the original height of 20000 m? Exercise 117 (a) -297 m/s (b) 3.66 m/s2 (c) 108 s