Acceleration = F/m implies Position = F/2m(t^2) + k1(t) + k2

That's quadratic, but definitely not exponential, and doesn't really look like the curve he drew.

I know the guy's argument doesn't really depend on the shape of the curve, but it's a pet peeve of mine that exponential growth is always presented in an inaccurate way.

EDIT: fixed embarrassing calculus error