Change in Motion and its Units

 There are some other terms like Acceleration, Jerk and Jounce which should have been studied before the essential concepts in physics. They were improved from the other terms such as displacement, velocity in the mechanics of motion.

Those terms like Acceleration, Jerk, and Jounce can be represented very simply using mathematics but it has a matter of to be understood thoroughly in a physical way.

For instance,

Acceleration is defined similar to the definition of velocity vector as,

Acceleration = Change in velocity vector / time,

 where the

              Velocity vector = Displacement vector / time (or) Change in position vectors/ time

Since Velocity is a vector quantity, ‘change in velocity’ that is ‘acceleration’ is also a vector quantity.

  

Similarly,        

                                    Jerk                 =          Change in acceleration vector/ time

and,                            

                                   Jounce             =          Change in Jerk vector / time

Note: You can ask whether it can be defined further as Change in Jounce vectors and etc.

Yeah it can be defined. But it is enough to describe most of the motions that happens in the universe using these terms. If you want to define, you can do. But it is up to Nature’s choice whether it is going to be used or not in real life problems.

There are given certain units for all these mechanical terms. It is called system of units. SI units are the most widely used unit system.  

As per the SI units,

                                                the fundamental unit of            length is          meter

and                                          the fundamental unit of            time      is          second.

Using the fundamental units all other units can be derived using simple arithmetic.

            Displacement is a vector that has only length and direction.

It should be noted that directions are always symbolized by writing separately near the physical quantities.  Therefore,

Unit of “displacement” is meter

and also                          Unit of “distance” is meter,     as they both are the measure of lengths.

Since displacement is measured in meters, change in displacement is also denoted using meters.

Unit of velocity vector = Unit of “change in position vectors”/ Unit of “time” (or)

Unit of “displacement vector”/ Unit of “time”

gives,                           Unit of velocity = meter/ second

and also                       Unit of speed = meter/ second,          as they both are the measure of rate of change of lengths.

Similarly, Unit of acceleration is derived as,

                       

Unit of Acceleration vector = Unit of “Change in velocity vectors” /Unit of “time” (or)

Unit of “Velocity vectors”/Unit of “time”

→                                Unit of Acceleration vector =  (meter/second)/second

→                                Unit of Acceleration vector =  (meter/second)* 1/second

→                                Unit of Acceleration vector =  meter/(second^2)

Correspondingly,        

Unit of Jerk vector = Unit of (acceleration vector / time ) = meter/ (second^3)

Unit of Jounce vector = Unit of (Jerk vector / time) = meter/ (second^4)

Thus Units were given for most of the physics terms using SI units.

Now, it was come to the situation of being a little bit saturated in the definitions of mechanics. And so now on, it will be discussed real life problems that can be solved using the above concepts. Also it will be discussed about the mathematical improvements that were made on the calculations of displacement, velocity, acceleration, etc.

            In future it will be seen that, those mathematical improvements made a very great evolution in the history of mathematics, called the differentiation and integration developed by the great scientists both Isaac Newton and Leibniz.