State and derive newton 's second …

The second law of motion states that the rate of change of momentum of an object is proportional to the applied unbalanced force in the direction of force.

The  quantity  of  motion  in  a  body depends  on  the product of mass  and  velocity  of  the  body termed as momentum.

The momentum (p) of a body is defined as the product of its mass (m) and velocity (v) and has the same direction as that of the velocity. Its SI unit is kilogram metre per second (kg m s−¹).

Momentum = mass × velocity

p = m × v

Momentum has both magnitude as well as direction; hence it is a vector quantity.

Momentum of a body at rest is zero.

Suppose an object of mass, m is moving along a straight line with an initial velocity, u. It is uniformly accelerated to velocity, v in time, t by the application of a constant force, F throughout the time, t. The initial and final momentum of the object will be, p1 = mu and p2 = mv respectively.

The change in momentum ∝ p2 – p1

∝ mv – mu

∝ m × (v – u).

The rate of change of momentum ∝ m × (v – u)/t

Or, the applied force,

F ∝ m × (v – u)/t

F = km × (v – u)/t

= kma

Here, a = [(v – u)/t ] is the acceleration, which is the rate of change of velocity. The quantity, k is a constant of proportionality.

The SI unit of mass and acceleration are kg and ms-2.

One unit of force is defined as the amount that produces an acceleration of 1 ms-2  in an object of 1 kg mass.

1 unit of force = k × (1 kg) × (1 ms-2).

The unit of force is kg ms-2 or newton, which has the symbol N. The second law of motion gives us a method to measure the force acting on an object as a product of its mass and acceleration.