MOTION IN A STRAIGHT LINE

INTRODUCTION

Motion is common to everything in the universe. We walk, run and ride a bicycle. Even when we are sleeping, air moves into and out of our lungs, and blood flows in arteries and veins. We see leaves falling from trees and water flowing down a dam. Automobiles and planes carry people from one place to the other. The earth rotates once every twenty-four hours and revolves around the sun once a year. The sun itself is in motion in the Milky Way, which is again moving within its local group of galaxies.

Motion is a change in the position of an object with time. How does the position change with time? In this chapter, we shall learn how to describe motion. For this, we develop the concepts of velocity and acceleration. We shall confine ourselves to the study of the motion of objects along a straight line, also known as rectilinear motion. For the case of rectilinear motion with uniform acceleration, a set of simple equations can be obtained. Finally, to understand the relative nature of motion, we introduce the concept of relative velocity. In our discussions, we shall treat the objects in motion as point objects. This approximation is valid so far as the size of the object is much smaller than the distance it moves in a reasonable duration of time. In a good number of situations in real-life, the size of objects can be neglected and they can be considered point-like objects without much error.

Motion in a straight line is a fundamental concept in physics that describes the movement of an object along a single path. This type of motion is found in a variety of everyday applications, from car travel to projectile motion, and is governed by the laws of physics. In this essay, I will explore the principles of motion in a straight line and how they are applied to everyday life. I will discuss linear motion, kinematic equations, and the concepts of acceleration and velocity. I will also analyze the various forces that act on an object in motion, including gravity and friction. Finally, I will explore the applications of motion in a straight line, such as in projectile motion and motion in a vacuum. By examining these principles and applications, I will demonstrate the importance of motion in a straight line in our everyday lives.

POSITION, PATH LENGTH AND DISPLACEMENT

Motion in a straight line is a common occurrence in everyday life, whether it be in the form of walking, running, or driving. This type of motion can be expressed in terms of position, path length, and displacement. In this essay, I will discuss the differences between position, path length, and displacement in relation to motion in a straight line. I will also explain how these three terms can be used to describe and analyze the motion of an object. Further, I will discuss the implications of these concepts and how they can be applied in everyday life. Finally, I will provide examples to demonstrate my points. Thus, the purpose of this essay is to explore the concepts of position, path length, and displacement in motion in a straight line.

Path length

Consider the motion of a car along a straight line. We choose the x-axis such that it coincides with the path of the car’s motion and origin of the axis as the point from where the car started moving, i.e. the car was at x = 0 at t = 0 (Fig. 3.1). Let P, Q and R represent the positions of the car at different instants of time. Consider two cases of motion. In the first case, the car moves from O to P. Then the distance moved by the car is OP = +360 m. This distance is called the path length traversed by the car. In the second case, the car moves from O to P and then moves back from P to Q. During this course of motion, the path length traversed is OP + PQ = + 360 m + (+120 m) = + 480 m. Path length is a scalar quantity — a quantity that has a magnitude only and no direction .

Displacement

It is useful to define another quantity displacement as the change in position. Let x1 and x2 be the positions of an object at time t 1 and t 2.

 Then its displacement, denoted by ∆x, in time ∆t = (t2- t1), is given by the difference between the final and initial positions : ∆x = x 2 – x 1 (We use the Greek letter delta (∆) to denote a change in a quantity.) If x2 > x1 , ∆x is positive; and if x 2< x1, ∆x is negative. Displacement has both magnitude and direction. Such quantities are represented by vectors. You will read about vectors in the next chapter. Presently, we are dealing with motion along a straight line (also called rectilinear motion) only. In one-dimensional motion, there are only two directions (backward and forward, upward and downward) in which an object can move, and these two directions can easily be specified by + and – signs. For example, displacement of the car in moving from O to P is : ∆x = x 2  – x 1= (+360 m) – 0 m = +360 m.