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

[Gaebril]

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.

 

[azizlwl]

Sketch a graph of velocity vs. time and calculate the area under the graph.

s=vt

You can start v₀ at any point and v_f too.

 

[rcgldr]

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