Read and reason
Two equations, different complexity
A linear position model has two coefficients: b and m in x=b+mt. A quadratic model has three: b, m and c in x=b+mt+ct². With uniformly accelerated ideal one-dimensional motion, c=a/2. If data are approximately linear, the simpler model may generalize well and preserve a straightforward interpretation. If data clearly curve, a quadratic may fit better within the domain.
Least squares is a calculation, not magic
For each candidate model, choose coefficients that minimize the sum over training points of (observed x − predicted x)². Squaring gives larger errors more influence and removes sign cancellation. The Model Detective computes normal-equation least-squares fits for provided well-conditioned sample times. It is not a general-purpose statistical package; do not apply it uncritically to large ill-conditioned datasets.
Why reserve the last observation?
If every measured value is used to choose the coefficients and then the same data are scored, flexibility generally helps the quadratic model. The studio therefore fits only the first five points and compares predictions on the sixth point at t=5 s. That sixth measurement is a very small validation sample and should not be overinterpreted; it demonstrates the principle of testing predictions outside the fitted observations.
Interpret the fitted physics
For a quadratic fit x=b+mt+ct², initial position is b, initial velocity is m and modeled constant acceleration is a=2c, provided the time origin is t=0 and the observed motion truly follows constant acceleration. A fitted linear slope m approximates constant velocity. Neither formula can establish friction, drag or force mechanisms without additional physical evidence.