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Newton's Second Law Of Motion

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Newton's second law of motion states as follows:

The rate of change of momentum of a body is directly proportional to the applied force and takes place in the direction in which the force acts.

Before continuing, let's see what momentum is

The momentum of a body is defined as the product of its mass and its velocity.

That is, the momentum of a body is equal to mv. With mass in kg and velocity in m/s, the Standard International (SI) unit of momentum is kgm/s.

Notice that the greater the momentum of a body, the greater the force it will exert on another body.

Now back to Newton's second law of motion:

Mathematically, Newton's second law of motion can be expressed as

Force α change in momentum/time

F α (mv-mu)/t

where F represents a force on a body of mass m causing it to change its velocity from u (initial velocity) to v (final velocity) over a time t.

Simplifying further, we have

F α m(v-u)/t

(v-u)/t is the rate of change of velocity, and is same as acceleration, a.

Therefore,                   F α ma,  and

F = kma, where k is the force constant. The SI unit of force is the Newton (N).

It is the force which acts on a body of 1kg, making it to accelerate by 1m/s2.

Therefore, when F is in Newtons, m in kg and a in m/s2,

F = ma

Or F = m(v-u)/t

See calculations of force based on Newton's second law of motion here.
See Newton's Third Law Of Motion