Question

how to derive inertia from 1st law of motion ?

Answer 1

Newton’s First law of motion is itself the Law of Inertia. It says that a body tends to be at rest or a body at constant motion will continue its motion unaltered, unless disturbed by an external force. But the Law of Inertia can itself be derived from the second law.

F = ma = m (dv/dt)

In absence of any external force, F = 0.

This implies,

dv/dt = 0 (Since, m cannot be zero)

Thus, v remains constant. Even, v = 0 is also a constant. Hence, Law of Inertia is derived.