Let an object of mass ‘m’ is moving along a straight line with initial velocity ‘u’. A constant force ‘F’ is applied in time ‘t’ to accelerate it and its final velocity becomes ‘v’.
Initial momentum, p1 = mu
Final momentum, p2 = mv
Change in momentum ∝ p2 - p1 ∝ mv – mu
∝m (v – u)
The rate of change of momentum = \(\frac{m(v-u)}{t}\)
Rate of change of momentum = force applied
Force ∝ \(\frac{m(v-u)}{t}\)
Force = k\(\frac{m(v-u)}{t}\)where k = proportionality constant
Force = kma where a = acceleration =\(\frac{m(v-u)}{t}\)
