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 vi. Further suppose it covers a distance ‘S’ meters in ‘t’ seconds when its velocity reaches some final value vf. 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 1st equation of motion,

Put this value in the above equation,

This is 2nd equation of motion.
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