State Newton's second law of motion. Hence derive the equation of motion F = ma from it.

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> [!TLDR]
> Newton's second law says force equals the rate of change of momentum; for a body of constant mass, this reduces directly to $F = ma$.
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> **Statement of Newton's second law**
> The rate of change of linear momentum of a body is directly proportional to the applied external force, and the change in momentum takes place in the direction of the applied force.
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> **Derivation of $F = ma$**
> Let a body of mass $m$ have momentum $\vec{p} = m\vec{v}$, where $\vec{v}$ is its velocity.
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> By Newton's second law:
> $$\vec{F} \propto \frac{d\vec{p}}{dt}$$
> $$\vec{F} = k\,\frac{d\vec{p}}{dt}$$
> where $k$ is a constant of proportionality.
>
> Substituting $\vec{p} = m\vec{v}$:
> $$\vec{F} = k\,\frac{d(m\vec{v})}{dt}$$
>
> If the mass $m$ of the body remains constant with time (as is true for ordinary mechanics, non-relativistic and no mass loss/gain): …

Q.State Newton's second law of motion. Hence derive the equation of motion F = ma from it.

Concept understanding — Newton Second Law

Newton's Second Law: The Law That Connects Force and Motion

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Q.State Newton's second law of motion. Hence derive the equation of motion F = ma from it.

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