Newton’s second law of motion: The rate of change of momentum of an object is proportional to the applied unbalanced force in the direction of the force.

Let us assume:

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 force,

F throughout the time ρ.

Initial momentum of the object = ρ₁ = mu

Final momentum of the object = ρ_{2 = mv}

The change in momentum \(\propto \rho_2 - \rho_1\)

∝ mv - mu = m(v - u)

The rate of change of momentum ∝ \(\frac{m(v - u)}{t}\)

Applied force F ∝ \(\frac{m(v - u)}{t}\)

F = \(\frac{km(v - u)}{t}\)

F = k ma

\(a = \frac{v - u}{t}\)

k = constant of proportionality

F = kg m/s² = Newton

Use of second law of motion in sports:

In cricket field, the fielder gradually pulls his hands backward while catching a ball. The fielder catches the ball and gives swing to his hand to increase the time during which the high velocity of the moving ball decreases to zero.

The acceleration of the ball is decreased and therefore the impact of catching the fast moving ball4s reduced.
If not done so, then the fast moving ball will exert large force and may hurt the fielder.