Welcome students
Now we talk about the next chapter kinematics. This chapter deals with a position, velocity and acceleration. In this chapter specifically we will deal, with kinematics in One dimension, that means when a body is travelling in straight line.
In the kinematics, we do not consider the cause of motion, which is used in next chapter. that is termed as dynamics. So in short in this chapter we talk about position, reference point, speed, velocity and acceleration. These are the terms which we should remember and understand not only for this chapter but throughout the study of physics. While you understand the cause of motion in the chapter dynamics. In this chapter of dynamics we study cause of motion
Now we define specific terms which will be important in understanding this chapter.
Rest and motion :
These are the two topics which are always relative to each other. When you are sitting in a bus and another passenger is sitting next to you, whatever is your velocity the other person feels that you are stationary. This is because he is also moving along with you in same direction with same speed hence for other person you are stationary. In other words you are at rest relative to him. Actually both are you are moving in same direction and same speed. Let us take one another example when you are moving in a bus at a given speed, i.e. assume that you are velocity is 60 km per hour and another bus coming from opposite side also has velocity of 60 km per hour. Now when both buses are moving opposite to each other you will find buses move very fast with respect to each other, and if both bus move in same direction they are relatively stationary, and not in motion.
Now Reference point and origin :
Origin is usually taken as the starting point, while the reference point is a point about which the motion can be described easily. For example if I have to come to your school, I may ask you the about school, where is the school? You might tell me how to reach your school giving me the map or you can also state any prominent place, any cinema hall or Shopping Complex or temple near your School. And then you explain me route from that prominent place. Now this prominent place should be known to both of us. This prominent place in physics is called as reference point, in many situation origin reference point are the same.
Distance and displacement :
Distance is the path actually travelled by a body, word displacement is shortest path between those two points. You can imagine displacement as the air route from Delhi to Chennai, but if you drive down you will not go in straight path because the road may be curved at many places. But the air route is to be a straight line, this confirms displacement can never be more than distance and if it is a straight line motion displacement and distance would be same. After understanding distance and displacement, you know that both of them are measured in length, their dimension is [L] and unit is meter.
So students after this we describe the term called speed, which is rate of change of distance. As discussed distance is either greater than equal to displacement and also velocity is defined as rate of change of displacement. Hence you can understand velocity can either be equal to speed or less than that. Velocity can never exceed the value of speed. I hope this clarifies because of the definition only.
Next is uniform velocity and non uniform velocity, firstly we should understand what does the word uniform and nonuniform means. A uniform motion is, which we say equal displacement in equal time. If it is a non uniform motion it means equal displacement in different time or different displacement in equal time, whatever you can understand. After uniform and nonuniform motion now let us think of of uniform and nonuniform acceleration. Uniform acceleration means rate of change of velocity is constant while non uniform acceleration means,, rate of change of velocity is not constant and is depending on time
Whatever equations we use in kinematics till now are termed as equation of uniformly accelerated motion. Thus whenever we have non uniform acceleration we cannot use these equations and we use calculus, differentiation and integration.
Now coming to graphical representation, what is graph, in general we draw the relation between two variables on plane of paper. We have got x axis and y axis on the graph. In usual kinematics equations add related graphs we normally, put time on x axis and other variable on y axis. we usually name graph as displacement versus velocity when displacement is on y-axis time is on axis. Similarly graph of velocity versus time will give me velocity on y axis and time on x axis
Any graph on y and x axis, we come across a new word called slope stop. The slope is basically tangent of the angle which the line makes with x axis. In other words is y divided by x. So when we have displacement versus time the slope will be upon time will give us velocity, when we have graph of velocity versus time its slope gives us velocity divided by time that is acceleration. And also area under the curve give the value of y multiplied by x. That means the area of velocity time graph will be the displacement. Most common graph in kinematics is velocity time graph, the slope of which acceleration area under curve give you displacement
Important thing to understand graph is, let us say in velocity time graph, if the graph is not a straight line, that means it is a curve, how do we calculate the slope. Now in such graph to find the slow at any point is not the same as of straight line. So in such a case slope at a point is found by drawing tangent at that point and finding the angle which tangent makes with x axis.
You may please download the graph which we are to solve on 31.05.19 at 4 pm