**Question 6:** Derive second equation of motion.

**ANSWER**

Second equation is derived with the help of the definition of average velocity and making use of the first equation of motion.

Let a body of mass ‘m’ is moving with an initial velocity v_{i}. Further suppose it covers a distance ‘S’ meters in ‘t’ seconds when its velocity reaches some final value v_{f}. Then ‘S’ is given by,

But the average velocity is given by

Put this value of average acceleration in the above equation for the distance covered,

Put this value of average acceleration in the above equation for the distance covered,

Now
from 1^{st} equation of motion,

Put this value in the above equation,

This is 2^{nd} equation of motion.

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