State Newton’s second law of motion. Derive a mathematical expression for Newton’s second law. 

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Newton's Second law of motion explains the definition of the  Force. 
Force {F} = Mass{M} * Acceleration of the object{A}
F=ma
or 
F=mass * Rate of the change of velocity / time taken 
 
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the force acting on the body is directly propotional to the product of its mass and accleration produced by the force in the body.
it gives the mathematical difination of force.
F=force
m=mass
a=accleration
then,
F  DIRECTLY PROPOTIONAL   ma
F=kma
if k=1        (k=constant)
then,    F=ma
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