Question

Show that Newton's first law of motion is contained in the second law of motion.

Answer 1

1. The first law of motion states that the position of an object, in motion or at rest, does not change unless some external force is applied to it.
2. So, if no external force is acting on the object, we can write, $F=0$.
3. From the second law of motion, $F=mxa$.
4. This gives,$a=\frac{F}{m}=\frac{0}{m}=0$.
5. $Acceleration=\frac{changeinvelocity}{timeinterval}=\frac{v-u}{t}$
6. Hence, $$\begin{gathered} \frac{v-u}{t}=0 \\ v-u=0 \\ v=u \end{gathered}$$
7. This means, that if no external force is applied to a moving object, then its initial and final velocities are equal.
8. That is, there is no change in the state of motion of the object.
9. This shows that the first law of motion is contained in the second law of motion.