# Derive 1-dimensional motion from average acceleration (no calculus)

## Main Question or Discussion Point

Starting with the expressions for average acceleration (Change in Velocity over Change in time), average velocity at constant acceleration; algebraically (NO CALCULUS) derive the equation for one-dimensional motion that relates displacement to the acceleration, assuming acceleration is constant.

Related Other Physics Topics News on Phys.org
Sketch a graph of velocity vs. time and calculate the area under the graph.

s=vt

You can start v0 at any point and vf too.

rcgldr
Homework Helper
It can be derived based on the fact that with constant acceleration, for any time period, the average velocity during that time period is 1/2 the sum of the initial and final velocity.

v0 = initial velocity
v1 = final velocity
v1 = v0 + at

average velocity = 1/2 (v0 + v1) = 1/2 (v0 + (v0 + at) = v0 + 1/2 a t

distance = initial position + average velocity x time

x = x0 + (v0 + 1/2 a t) t = x0 + v0 t + 1/2 a t2