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,
![](https://mashalscienceacademy.com/wp-content/uploads/2021/08/e13c3p11.png)
But the average velocity is given by
![](https://mashalscienceacademy.com/wp-content/uploads/2021/08/e14c3p11.png)
Put this value of average acceleration in the above equation for the distance covered,
![](https://mashalscienceacademy.com/wp-content/uploads/2021/08/e15c3p11.png)
Put this value of average acceleration in the above equation for the distance covered,
![](https://mashalscienceacademy.com/wp-content/uploads/2021/08/e16c3p11.png)
Now
from 1st equation of motion,
![](https://mashalscienceacademy.com/wp-content/uploads/2021/08/e17c3p11.png)
Put this value in the above equation,
![](https://mashalscienceacademy.com/wp-content/uploads/2021/08/e18c3p11.png)
This is 2nd equation of motion.
Pingback:force-and-motion – msa