Deriving the Equation for Final Velocity Using Kinematic Equations

[zeion]

Homework Statement

I wanted to know how this equation is derived. Thanks.

Homework Equations

$${v_{f}}^2 = {v_{i}}^2 + 2a\Delta d$$

The Attempt at a Solution

$$v_{f} - v_{i} = \frac {\Delta d a} {\Delta v}$$

 

[Fightfish]

We have the two relations:
$$t=\frac{v-u}{t}$$
$$s=\frac{1}{2}(u+v)t$$

Substitute the first into the second and the deed is done.

 

[bp_psy]

Start from:
1. v=vo+at
2. r=ro+vo*t+(at^2)/2
Find t from 1 and replace in 2, do all the algebra and you are done.