Chapter 2 Kinematics in One Dimension
There are two aspects to any motion. In a purely descriptive sense, there is the movement itself. Is it rapid or slow, for instance? Then, there is the issue of what causes the motion or what changes it, which requires that forces be considered. Kinematics deals with the concepts that are needed to describe motion. without any reference toforces. The present chapter discusses these concepts as they apply to motion in one dimension, and the next chapter treats two-dimensional motion. Dynamics deals with the effect that forces have on motion, a topic that is considered in Chapter 4. Together, kinematics and dynamics form the branch of physics known as mechanics. We turn now to the ﬁrst of the kinematics concepts to be discussed,which is displacement. To describe the motion of an object, we must be able to specify the location of the object at all times, and Figure 2.1 shows how to do this for one-dimensional motion. In this drawing, the initial position of a car is indicated by the vector labeled x 0 . The length of x 0 is the distance of the car from an arbitrarily chosen origin. At a later time the car has moved to a newposition, which is indicated by the vector x. The displacement of the car x (read as “delta x” or “the change in x”) is a vector drawn from the initial position to the ﬁnal position. Displacement is a vector quantity in the sense discussed in Section 1.5, for it conveys both a magnitude (the distance between the initial and ﬁnal positions) and a direction. The displacement can be related to x 0 andx by noting from the drawing that x0 x x or x x x0
Displacement = ∆x x
Figure 2.1 The displacement
x is a
vector that points from the initial position x0 to the ﬁnal position x.
Thus, the displacement x is the difference between x and x 0 , and the Greek letter delta ( ) is used to signify this difference. It is important to note that the change in anyvariable is always the ﬁnal value minus the initial value.
I DEFINITION OF DISPLACEMENT
The displacement is a vector that points from an object’s initial position to its ﬁnal position and has a magnitude that equals the shortest distance between the two positions. SI Unit of Displacement: meter (m) The SI unit for displacement is the meter (m), but there are other units as well, such as thecentimeter and the inch. When converting between centimeters (cm) and inches (in.), remember that 2.54 cm 1 in. Often, we will deal with motion along a straight line. In such a case, a displacement in one direction along the line is assigned a positive value, and a displacement in the opposite direction is assigned a negative value. For instance, assume that a car is moving along an east/west directionand that a positive ( ) sign is used to denote a direction due east. Then, x 500 m represents a displacement that points to the east and has a magnitude of 500 meters. Conversely, x 500 m is a displacement that has the same magnitude but points in the opposite direction, due west.
2.2 Speed and Velocity
One of the most obvious features of an object in motion is how fast it ismoving. If a car travels 200 meters in 10 seconds, we say its average speed is 20 meters per second, the
20 Chapter 2 Kinematics in One Dimension average speed being the distance traveled divided by the time required to cover the distance: Average speed Distance Elapsed time (2.1)
Equation 2.1 indicates that the unit for average speed is the unit for distance divided by the unit for time, ormeters per second (m /s) in SI units. Example 1 illustrates how the idea of average speed is used.
Example 1 Distance Run by a Jogger
How far does a jogger run in 1.5 hours (5400 s) if his average speed is 2.22 m /s?
Reasoning The average speed of the jogger is the average distance per second that he travels. Thus, the distance covered by the jogger is equal to the average distance per...
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