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 OneDimensional 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 non-uniform velocity, an xversus-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 Ex. 2.7 Two riders on dune buggies sit 10 m apart on a long straight track, facing in opposite directions. Starting at the same time, both riders accelerate at a costant rate of 2.0 m/s2. How far apart will the dune buggies be at the end of 3.0s? Figure 2-11 Away they go! Example 2.8 The stopping distance of a vehicle is an important factor in road safety. This distance depends on the initial velocity (vo) and the braking capacity which produces the deceleration, a., assumed to be constant. Express the stopping distance x in terms of these quantities. Figure 2-12 Vehicle stopping distance 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 Ex. 2.11 A worker on a scaffold in front of a billboard throws a ball straight up. The ball has an initial speed of 11.2 m/s, when it leaves the worker’s hand. (a) What is the maximum height the ball reaches relative to the top of the billboard? (b) How long does it take the ball to reach this height? (c) What is the position of the ball at t = 2.0 s? Figure 2-19 Speed versus velocity 13. An insect crawls along the edge of a rectangular swimming pool of length 27 m and width 21 m. If it crawls from corner A to corner B in 30 min, (a) what is its average speed and (b) what is its average velocity? Figure 2-20 Position versus time 14. A plot of position versus time is shown in Fig. 2.20 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? Figure 2-21 Position versus time 15. In demonstrating a dance step, a person moves in one dimension, as shown in Fig. 2.21. What are (a) the average speed and (b) the average velocity for each phase of the motion? (c) What are the instantaneous velocities at 2.5 s, 4.5 s, and 6.0 s? (d) What is the average velocity for the interval between and [Hint: Recall that the overall displacement is the displacement between the starting point and the ending point.] Figure 2-22 When and where do they meet? 22. Two runners approaching each other on a straight track have constant speeds of and respectively, when they are 100 m apart (Fig. 2.22). How long will it take for the runners to meet, and at what position will they meet if they maintain these speeds? Figure 2-21 Description of motion Figure 2-23 Velocity versus time 33. What is the acceleration for each graph segment in Fig. 2.23? Describe the motion of the object over the total time interval. Figure 2-23 Velocity versus time Figure 2-24 Hit the professor Figure 2-25 From where did it come? 77. 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 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.) Figure 2-27. A tie race Figure 2-28 Down she comes