F = ma
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Answers
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
The change in momentum = mv – mu
The change in momentum = m × (v – u).
The rate of change of momentum = m × (v – u)/t(v - u)t
Or, the applied force, F ∝ m × (v – u)/t (v - u)t
F = km × (v – u)/t
F = kma _____ (i)
Here, a is the acceleration [i.e., a= (v – u)/t], which is the rate of change of velocity. The quantity, k is a constant of proportionality.
The SI units of mass and acceleration are kg and m s-2 respectively. The unit of force is so chosen that the value of the constant, k becomes one. For this, one unit of force is defined as the amount that produces an acceleration of 1 m s-2 in an object of 1 kg mass. That is,
1 unit of force = k × (1 kg) × (1 m s-2).
Thus, the value of k becomes 1.
From Eq. (i)
F = ma
The unit of force is kg m s-2 or newton, represented as N.
PLS MARK BRAINLIEST
