Question

State Newton's second law of motion and derive its mathematical.​

Answer 1

Answer:

Newton’s second law of motion can be formally stated as follows: 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.

Explanation:

Consider a body of mass m moving with initial velocity u. Let a force F acts on the body for time t so that the velocity of the body after time t is v.

Initial momentum = mu

Final momentum = mv

Now,

Change in momentum = mv - mu

= m(v-u)

Time taken to change this momentum = (t-0)

= t

Therefore,

Rate of change of momentum = Change in momentum/ Time taken

= m(v-u) / t

According to the definition of Newton's second law of motion,

Force applied is directly proportional to rate of change of momentum

Or, F is directly proportional to

m(v-u)/t.................(1)

Since v= u+at or (v-u/t) = a

Therefore, eqn. 1 can be written as

F is directly proportional to ma

Or, F= kma...........(2)

Where k is constant of proportionality

If F = 1 unit

m = 1 unit

And, a = 1 unit

Then from eqn (2),

1 = k or k= 1

Put this value of k = 1 in eqn 2, we get,

F= ma

Thus, force acting on the body is directly proportional to

• It's mass

• It's acceleration