Question

state Newton's second law of motion and show that the first law of motion can be mathematically stated from the mathematical expression for the second law of motion

Answer 1

HEY BUDDY !!!


HERE IS UR ANSWER!!!


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♤ Second law of Newton states that force applied on a body is equal is equal to change in momentum , i.e

=》 F = d( P ) / dt

● We know P = m.v

● Where , m is mass of body ; v id velocity

=》 F = d( m.v ) / dt

=》 F = m.d( v ) / dt // mass always constant

■ We know ( d( v ) / dt ) is equal to acceleration


=》 F = m.a-----------( 1 )

■ First law states that if no force is applies object , it doesn'tchange it's state .


■ Now in eqn ( 1 ) putting F = 0

■ There fore acceleration will be 0 , which means object is in rest or have constant velocity.Hence it proves first law of motion.


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Answer 2

$\large \leadsto\underline{\boxed{\blue{ \pmb{ \bf{Newton's \: second \: law \: of \: motion}}}} }$

Newton’s Second Law states that the acceleration of an object depends upon two variables – the net force acting on the object and the mass of the object.

• The acceleration of the body is directly proportional to the net force acting on the body and inversely proportional to the mass of the body.
• This means that as the force acting upon an object is increased, the acceleration of the object is increased. Likewise, as the mass of an object is increased, the acceleration of the object is decreased.

Newton’s second law can be formally stated as,

• The acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object.

Above statement is expressed in equation form as,

a = Fnet/m

F = ma