Why is average velocity multiplied by 2 to get final velocity?

[Lovely]

I have searched for this answer all day long.
Why is Vave multiplied by 2 to obtain Vf?

 

[sharans]

i feel Vave=(Vf+Vi)/2
since Vi=0,we have the result.

 

[Gokul43201]

Going by the definitions, we have, for the average velocity :

$$v_{ave} = \frac{total~distance~traveled}{total~time~taken} = \frac {s}{t}$$


Now just substitute for s, from the equations of motion to get the required result.