Let, ‘m’ be the mass of a moving body, moving along a straight line with an initial speed V. After a time interval of ‘t’, the velocity of the body changes to v due to the impact of an unbalanced external force F.
Initial momentum of the body Pi = mu
Final momentum of the body Pf = mv
Change in momentum Δp = Pi – Pf – mv – mu
By Newton’s second law of motion,
Force, F ∝ rate of change of momentum
F ∝ change in momentum / time
F ∝ \(\frac{mv - mu}{t}\)
F = \(\frac{km(v-u)}{t}\)
Here, k is the proportionality constant.
k = 1 in all systems of units. Hence,
F = \(\frac{m(v-u)}{t}\)
Since,
acceleration = change in velocity/time,
a = (v – u)/t.
Hence, we have F = m × a
Force = mass × acceleration
