Question

Mathematically show how Newton's 1st law is a special case of Newton's second law?

Answer 1

the second law of motion states that acceleration of a particle ( measured from inertial frame ) is given by resultant of all the forces acting on it divided by its mass
mathematically it is represented as
a=Fr/m note acceleration and force is a vector quantity
here Fr is resultant force
we write above equation as
Fr=ma
first law states that if the body remains accelerated then the sum of all the forces acting on the body is zero
i.e. Fr=0 where acceleration is a=0
thus we can obtain first law by keeping the value of acceleration (a) 0 in second law
Hence first law is a special case of second law where acceleration is 0
Hope this helped u :-)

Answer 2

Newton's first law states that every object will remain at rest or in uniform motion in a straight line unless compelled to change its state by the action of an external force. This is normally taken as the definition of inertia.