Prove the force = mass x acceleration. State the condition when it holds.

The rate of change of momentum = Δp/Δt = Δ(mv)/Δt

(When vc or m is not constant). But if mass m is constant i.e., v

rate of change of momentum = Δp/Δt = m Δv/Δt

Here the quantity Δv/Δt= rate of change of velocity i.e., acceleration a.

Rate of change in momentum = Δp/Δt= m Δp/Δt = ma

Thus, by Newton's second law of motion,

F ∝ ma

or, F= k ma

Where k is a constant of proportionality which can be made equal to 1 by choosing the suitable unit for force.

Hence, F = ma when mass m of the body is constant at velocity v which is much smaller than the velocity of light.