Question

Prove that vf = vi+at.

Answer 1

To make your formula neater:

$V_{f} = V_{i} + a*t$

Acceleration is equal to

$\frac{velocity}{time}$ ,

so when you multiply it by time, you will get a velocity.  In fact, you would get the change in velocity, as a*t signifies the acceleration of the object over the time, aka the change in velocity.

The initial velocity plus the change in velocity will equal the final velocity, irregardless if the change in velocity is positive or negative.

Therefore,

$V_{f} = V_{i} + a*t$