H H Chapter 2 - Motion in a Straight Line

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There are two aspects to any motion.

      Kinematics deals with the concepts that are needed to describe motion, without any reference to forces. 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.

A Grapical Representation of One-Dimensional Motion

From the Position-Time Graph one can derive the speed of an object from the slope of the curve.

Average Velocity and Instantaneous Velocity

Motion Graphs and Derivatives

Finding the tangent to a curve

Mechanical Universe (click on diagram below)

Click on diagram below to practice recognizing the graphs

The slope at any point along the curve in the position-time graph will be the velocity.

Looking at the acceleration and velocity vectors

The slope at any point
along the position - time curve will represent the velocity at that point.

The slope at any point
along the velocity - time curve will represent the acceleration at that point.

Motion I, II, III

Below is an example of how to solve a problem.
Watch it develop.

Derivation of the Motion Equations
Click to see the derivation

Reasoning Strategy (creating a neural net)

Applying the Equations of Kinematics

1. Make a neat and complete drawing to represent the situation being studied. A drawing helps us to visualize what's happening. This is where you will discover if you understand the question.

2. Draw a coordinate axis system and decide which directions are to be called positive (+) and negative (-) relative to a conveniently chosen coordinate origin.

3. In an organized way, write down the values (with appropriate plus and minus signs) that are given for any of the five kinematic variables (x, a, v, v0 , and t). Be on the alert for implicit data, such as the phrase “starts from rest,” which means that the value of the initial velocity is . The data summary boxes used in the examples in the text are a good way of keeping track of this information. In addition, explicitly identify the variables that you are being asked to determine.

4. Before attempting to solve a problem, verify that the given information contains values for at least three of the five kinematic variables. Once the three known variables are identified along with the desired unknown variable, the appropriate motion equation can be selected. Remember that the motion of two objects may be interrelated, so they may share a common variable. The fact that the motions are interrelated is an important piece of information. In such cases, data for only two variables need be specified for each object.

5. When the motion of an object is divided into segments, as in Example 9, remember that the final velocity of one segment is the initial velocity for the next segment.

6. Keep in mind that there may be two possible answers to a kinematics problem as, for instance, in Example 8. Try to visualize the different physical situations to which the answers correspond.

Reaction time and the Motion Equations




Problem Solving

Mechanical Universe - Freefall