Question
Newton’s first law is contained in the second law. Prove it.
✓
Answer
1. From Newton's second law of motion, we have,
$\overrightarrow{ F }=\frac{ d \overrightarrow{ p }}{ dt }=\frac{ d }{ dt }( m \overrightarrow{ V })$
2. For a given body, mass $m$ is constant.
$\therefore \overrightarrow{ F }= m \frac{ d \overrightarrow{ V }}{ dt }= m \overrightarrow{ a }$
3. If $\vec{F}=$ zero, $\vec{V}$ is constant. Hence if there is no force, velocity will not change. This is nothing but Newton's first law of motion.
$\overrightarrow{ F }=\frac{ d \overrightarrow{ p }}{ dt }=\frac{ d }{ dt }( m \overrightarrow{ V })$
2. For a given body, mass $m$ is constant.
$\therefore \overrightarrow{ F }= m \frac{ d \overrightarrow{ V }}{ dt }= m \overrightarrow{ a }$
3. If $\vec{F}=$ zero, $\vec{V}$ is constant. Hence if there is no force, velocity will not change. This is nothing but Newton's first law of motion.
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