Let's take a special case of one-dimensional motion with constant force (derivation equally applies to vector) - fan cart moving under constant fan force
Write out prediction equations: show prediction of final velocity. This net force over m is acceleration - kinematic equation to predict velocity from observation (graph of v vs t)
Discuss average velocity - displacement version and arithmetic: use previous equation to calculate average v
plug into position prediction equation: obtain 2nd kinematic equation (graph of x vs t) - emphasize exactness of the equations b/c constant force