Question

prove newton's first law of motion using newton's second law of motion

Answer 1

to prove : newtons 1st law:if the force acting on an object is zero the object in motion will be in motion the object at rest will be at rest.

according to newtons second law
F=m*a
if F=0
m*a=0
since mass can never be equal to zero because if it is zero it do not exist
so a=0
if a =0
two things can happen

1)the object is at rest
a=Δv/Δt
 if Δv=0 the object is at rest

2) the object is at constant velocity
if velocity is constant Δv=0
a=Δv/Δt therefor a=0.

hence proved
if the force acting on an object is zero 1)the object is at rest will be at rest 2)the object in motion will be in motion.

Answer 2

To prove :

Newton's first law of motion using Newton's second law of motion

Proof :

• Newton's second law : It states that rate of change of momentum is directly proportional to the force applied.

$\sf{F = ma} \: \: \: \: \: \: \: \: \: (a = \frac{v - u}{t} )$

$\sf{F= m \times \frac{v - u}{t} } .......(i)$

If there is no force applied

F = 0

From equation (i) :-

$\sf{0 = m \times \frac{v - u}{t} }$

$\sf{ \frac{v - u}{t} = 0 }$

$\sf{v - u = 0}$

$\boxed{\sf{v = u}} ..... \sf{(ii)}\green \bigstar$

Final velocity = Initial velocity

If initially the body is at rest

$\sf{u = 0}$

From equation (ii) :-

$\sf{v = u \times 0}$

$\sf{v = 0} \: ....(iii)$

From equation (ii) and (iii) it is proved that first law of motion lies in the second law of motion..