In a moment the arresting cable will be pulled taut, and the 140-mi/h landing of this F/A-18 Hornet on the aircraft carrier USS Nimitz will be brought to a sudden conclusion. The pilot cuts power to the engine, and the plane is stopped in less than 2 s. If the cable had not been successfully engaged, the pilot would have had to take off quickly before reaching the end of the ﬂightdeck. Can the motion of the plane be described quantitatively in a way that is useful to ship and aircraft designers and to pilots learning to land on a “postage stamp?” (Courtesy of the USS Nimitz/U.S. Navy)
c h a p t e r
Motion in One Dimension
2.1 2.2 2.3 2.4 2.5
Displacement, Velocity, and Speed Instantaneous Velocity and Speed Acceleration Motion DiagramsOne-Dimensional Motion with Constant Acceleration
2.6 Freely Falling Objects 2.7 (Optional) Kinematic Equations
Derived from Calculus
GOAL Problem-Solving Steps
Motion in One Dimension
s a ﬁrst step in studying classical mechanics, we describe motion in terms of space and time while ignoring the agents that caused that motion. This portion of classical mechanics iscalled kinematics. (The word kinematics has the same root as cinema. Can you see why?) In this chapter we consider only motion in one dimension. We ﬁrst deﬁne displacement, velocity, and acceleration. Then, using these concepts, we study the motion of objects traveling in one dimension with a constant acceleration. From everyday experience we recognize that motion represents a continuous change in theposition of an object. In physics we are concerned with three types of motion: translational, rotational, and vibrational. A car moving down a highway is an example of translational motion, the Earth’s spin on its axis is an example of rotational motion, and the back-and-forth movement of a pendulum is an example of vibrational motion. In this and the next few chapters, we are concerned only withtranslational motion. (Later in the book we shall discuss rotational and vibrational motions.) In our study of translational motion, we describe the moving object as a particle regardless of its size. In general, a particle is a point-like mass having inﬁnitesimal size. For example, if we wish to describe the motion of the Earth around the Sun, we can treat the Earth as a particle and obtainreasonably accurate data about its orbit. This approximation is justiﬁed because the radius of the Earth’s orbit is large compared with the dimensions of the Earth and the Sun. As an example on a much smaller scale, it is possible to explain the pressure exerted by a gas on the walls of a container by treating the gas molecules as particles.
Position of the Car at Various TimesPosition t(s) 0 10 20 30 40 50 x(m) 30 52 38 0 37 53
DISPLACEMENT, VELOCITY, AND SPEED
The motion of a particle is completely known if the particle’s position in space is known at all times. Consider a car moving back and forth along the x axis, as shown in Figure 2.1a. When we begin collecting position data, the car is 30 m to the right of a road sign. (Let us assume that all data in thisexample are known to two signiﬁcant ﬁgures. To convey this information, we should report the initial position as 3.0 101 m. We have written this value in this simpler form to make the discussion easier to follow.) We start our clock and once every 10 s note the car’s location relative to the sign. As you can see from Table 2.1, the car is moving to the right (which we have deﬁned as the positivedirection) during the ﬁrst 10 s of motion, from position to position . The position values now begin to decrease, however, because the car is backing up from position through position . In fact, at , 30 s after we start measuring, the car is alongside the sign we are using as our origin of coordinates. It continues moving to the left and is more than 50 m to the left of the sign when we stop...