Welcome once again students
Now in this episode we talk about the next chapter, which is kinematics. Kinematics is divided into two parts motion in One dimension and motion in two dimensions. Firstly we will discuss motion in one dimension.
You are aware that we are having three equations of motion, which we have been using for long time. Always remember that the technical name of these equations is, motion of uniformly accelerated motion. That simply means that in all these equations acceleration has to be constant. If acceleration is not constant we cannot use these equations.
v = u + at,
s = ut + 1/2 at2,
v2 = u2 +2as.
Snth = u + (a/2)(2n-1)
Here I give you one more equation, which can be used much efficiently if a body has final velocity zero. i.e. it is stopped
s = vt – (1/2)at2
When acceleration is not constant, we will have to use calculus to get the answers. Please recall that the differentiation of displacement, gives velocity and differentiation of velocity gives acceleration. And similarly when we have to get displacement from velocity equation we will have to integrate, also when we want to find the change in velocity we will have to integrate the acceleration .
After these equations you should always keep in mind the study of graph . In fact the sign convention used in velocity equations are also based on graphical system . That means on the right side we have positive and on the left side we have negative . Similarly up words we take positive and downwards we take negative.
With the help of this graphical sign convention it becomes much easier to find the velocity and displacement . One more thing you should keep in mind that equations are for velocity and not for Speed . Similarly the equations are for Displacement and not for distance.
DOWN LOAD GLIMPSES of GRAPH if not Clear
Now it is important to understand the use of graphical system as well . we normally have time on x axis and velocity, speed, displacement or distance on y axis. The angle which the tangent to the curve makes with positive axis is called slope. Now you should understand that the slope of velocity time graph give the acceleration, and the slope of distance time graph give the speed, also the slope of displacement time graph gives idea of velocity.
At last we should also try to understand the meaning of area under the curve. the area under the curve is basically the product of x axis and y axis. hence the area under velocity time graph give the displacement, area under acceleration time graph gives change in velocity.