Question

how do we derive the formula at=vf-vi if we will find acceleration? please have it step by step. Thank you

Answer 1

we do it the same way we figure the average speed. Divide the distance covered (∆s) by the time taken (∆t).

For acceleration, it's the same. The average acceleration is the change in speed (∆v = vf-vi) by the amount of time it takes to make the change (∆t).

a = ∆v/∆t
a*∆t = ∆v

if we start at t=0, then ∆t = t, the time taken:

at = ∆v = vf-vi

or, think about what constant acceleration means. Each second, the velocity changes by a fixed amount (the acceleration). So, after t seconds, the velocity has changed by at. But the amount changed is ∆v = vf-vi. SO,

at = vf-vi