Let us consider an object of mass m, moving along a straight line with an initial velocity of u. Let us say, after a certain time t, with a constant acceleration, the final velocity becomes v.
Here we see that, the initial momentum is:
(p1) = m × u
The final momentum
(p2) = m× v
The change in momentum can be written as,
(p2 - p1) = (m × v) - (m × u) = m(v-u)
As we know, the rate of change of momentum with respect to time is proportional to the applied force. The applied force,
F ∝ [(m×v -u)] / t
or
F ∝ m×a
as acceleration (a) = rate of change of velocity with respect to time
F = k×m×a
Above is the second law of motion formula.
F is the force
k is the constant of proportionality
a is the acceleration
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