Newton's second Law of Motion states that The rate of change of momentum is directly proportional to the force applied in the direction of force.
For example; when acceleration is applied on a moving vehicle, the momentum of the vehicle increases and the increase is in the direction of motion because the force is being applied in the direction of motion. On the other hand, when brake is applied on the moving vehicle, the momentum of the vehicle decreases and the decrease is in the opposite direction of motion because the force is being applied in the opposite direction of motion.
Let mass of an moving object = `m`.
Let the velocity of the object changes from `'u'`; to `'v'` in the interval of time `'t'`
Initial velocity of the object = `u`.
Final velocity of the object = `v`.
We know that momentum (p) = Mass x velocity
Momentum (p) of the object at its initial velocity `u = m xx u = m\u`
Momentum (p) of the object at its final velocity `v = m xx v = mv`
The change in momentum `= mv - m\u`
Rate of change of momentum `=(mv-m\u)/t`-----(i)
According to the Newton’s Second Law of motion force is directly proportional to the rate of change of momentum.
This means, Force ∝ Rate of change of moentum
After substituting the value of rate of change of momentum from equation (i) we get.
Force (F) `prop (mv-m\u)/t`
`=>F prop (m(v-u))/t`
`=>F prop m(v-u)/t`
`=>F prop m a`
[∵ acceleration (`a`)`=(v-u)/t`]
[Since, acceleration is the rate of change in velocity]
Where `k` is the proportionality constant
∵ 1 unit force is defined as the mass of 1kg object produces the acceleration of 1m/s2
∴ 1 unit of force `=kxx1 kg xx 1m//s^2`
∴ by putting the value of `k=1` in equation (ii)
`F = m*a`----(iii)
⇒ Force = mass x acceleration
Thus Newton’s Second Law of Motion gives the relation between force, mass and acceleration of an object.
According to the relation obtained above, Newton’s Second Law can be modified as follows:
The product of mass and acceleration is the force acting on the object.
Since Force = Mass x Acceleration
The unit of mass = kg and The unit of acceleration = m/s2
If force, mass and acceleration is taken as 1 unit.
1 Newton (N) = 1kg x 1m/s2
Thus, Newton (N) = kg m/s2
Equation (v) can be also written as
This equation is the form of Newton’s Second Law of Motion. According to this equation, Newton’s Second Law of Motion can also be stated as follow:
The acceleration produced by a moving body is directly proportional to the force applied over it and inversely proportional to the mass of the object.
From the above relation it is clear that
Acceleration increases with increase in force and vice versa.
Acceleration decreases with increase in mass and vice versa.
That’s why a small vehicle requires less force to attain more acceleration while a heavy vehicle requires more force to get the same acceleration.
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