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DIFFERENTIALS HAVE A GREAT APPLICATION IN PHYSICS

DERIVATIVES ARE INVOLVED IN BERNOULLIS

EQUATION,EULERS EQUATION,EINSTEIN THORY,LAPLACEEQUATION,PROJECTILE MOTION ,STOKES LAW AND

ETC,SIMILARLYNEWTONS LAWS OF MOTION, NEWTON'S LAW

OF UNIVERSAL GRAVITATION,THE LAW OF CONSERVATION

OF ENERGY, THE LAW OF POPULATION GROWTH,ECOLOGICAL POPULATION COMPETITION, INFECTIOUS

DISEASES, GENETIC VARIATION, STOCK TRENDS, INTEREST

RATES AND THE MARKET EQUILIBRIUM PRICE CHANGES.

PEOPLE ATTRIBUTE THE UNDERSTANDING AND ANALYSIS

OF THESE PROBLEMS TO THE STUDY OF THE

CORRESPONDING ORDINARY DIFFERENTIAL EQUATIONS TO

DESCRIBE THE MATHEMATICAL WIDELY USED IN VARIOUS

FIELDS OF SOCIAL SCIENCE

http://en.wikipedia.org/wiki/Newtons_laws_of_motionhttp://en.wikipedia.org/wiki/Newton's_law_of_universal_gravitationhttp://en.wikipedia.org/wiki/Newton's_law_of_universal_gravitationhttp://en.wikipedia.org/wiki/The_law_of_conservation_of_energyhttp://en.wikipedia.org/wiki/The_law_of_conservation_of_energyhttp://en.wikipedia.org/wiki/The_law_of_conservation_of_energyhttp://en.wikipedia.org/wiki/The_law_of_conservation_of_energyhttp://en.wikipedia.org/wiki/The_law_of_conservation_of_energyhttp://en.wikipedia.org/wiki/The_law_of_conservation_of_energyhttp://en.wikipedia.org/wiki/The_law_of_conservation_of_energyhttp://en.wikipedia.org/wiki/Newton's_law_of_universal_gravitationhttp://en.wikipedia.org/wiki/Newton's_law_of_universal_gravitationhttp://en.wikipedia.org/wiki/Newtons_laws_of_motionhttp://en.wikipedia.org/wiki/Newtons_laws_of_motionhttp://en.wikipedia.org/wiki/Newtons_laws_of_motion

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An impulseJ occurs when a force F acts over an interval of time t, andit is given by

Since force is the time derivative of momentum, it follows that

This relation between impulse and momentum is closer to Newton's wording ofthe second law.

Impulse is a concept frequently used in the analysis of collisions and impacts.

http://en.wikipedia.org/wiki/Impulse_(physics)http://en.wikipedia.org/wiki/Impulse_(physics)http://en.wikipedia.org/wiki/Impulse_(physics)http://en.wikipedia.org/wiki/Impulse_(physics)http://en.wikipedia.org/wiki/Impulse_(physics)http://en.wikipedia.org/wiki/Impulse_(physics)http://en.wikipedia.org/wiki/Impulse_(physics)http://en.wikipedia.org/wiki/Impulse_(physics)http://en.wikipedia.org/wiki/Impulse_(physics)http://en.wikipedia.org/wiki/Impulse_(physics)http://en.wikipedia.org/wiki/Impulse_(physics)

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The second law states that the net force on a particle is equal to the time rate of

change of its linear momentum p in an inertial reference frame

where, since the law is valid only for constant-mass systems, the mass can be taken outside

the differentiation operator by the constant factor rule in differentiation. Thus,

where F is the net force applied, m is the mass of the body, and a is the body's

acceleration. Thus, the net force applied to a body produces a proportional

acceleration. In other words, if a body is accelerating, then there is a force on it

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IN CALCULUS

Calculus is of vital importance in physics: many

physical processes are described by equations

involving derivatives, called differential equations.

Physics is particularly concerned with the wayquantities change and evolve over time, and the

concept of the "time derivative"the rate of change

over timeis essential for the precise definition of

several important concepts. In particular, the time

derivatives of an object's position are significant

in Newtonian physics

http://en.wikipedia.org/wiki/Differential_equationhttp://en.wikipedia.org/wiki/Time_derivativehttp://en.wikipedia.org/wiki/Newtonian_physicshttp://en.wikipedia.org/wiki/Newtonian_physicshttp://en.wikipedia.org/wiki/Newtonian_physicshttp://en.wikipedia.org/wiki/Newtonian_physicshttp://en.wikipedia.org/wiki/Time_derivativehttp://en.wikipedia.org/wiki/Differential_equation

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VELOCITY AND ACCELARATION

Velocity

velocity is the

derivative (with respect

to time) of an object'sdisplacement (distance

from the original

position)

V=ds/dt

Acceleration

Acceleration is

the derivative (with

respect to time) of anobject's velocity, that is,

the second derivative

(with respect to time) of

an object's position.

a=dv/dt

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FOR EXAMPLE

For example, if an object's position on a line is given by

then the object's velocity is

and the object's acceleration is

which is constant.