Please explain different terms of this equation

The point marked in the cloud..

I am not able to understand the last term 2m[v'w]. What does this signify

carolies force its a pseudo force for more indepth go to jee advanced 2016 problem

  • \color{red} see {after} 17 minute

@Shwetanshu_2018 bro please explain in more indepth if possible..