Algebra is calculus, with the work already done.

Physics at whichever altitude you need. Learn algebra-based physics cleanly on its own terms — or see the same physics as calculus, and watch the algebra formulas fall out of the integrals.

A ball thrown straight up (up positive, g = −10 m/s²):

\begin{aligned} a(t) &= -10 && \text{(constant)} \\ v(t) &= \textstyle\int a\,dt = v_0 - 10t && \text{(a line; its slope is } a) \\ x(t) &= \textstyle\int v\,dt = x_0 + v_0 t - 5t^2 && \text{(a parabola; slope is } v\text{, area under } v \text{ is its change)} \end{aligned}

The algebra formulas v = v₀ + at and x = x₀ + v₀t + ½at² are those integrals with the acceleration frozen to a constant. Quadrature is the old word for evaluating an integral — finding the area under a curve. The constant-acceleration formulas are quadratures.

The graph is the pivot

On a stacked x–t / v–t / a–t plot with a shared time axis, the slope of the upper graph is the value of the lower, and the area under the lower is the change in the upper. Slope is the derivative; area is the integral. That is where the student with slope-and-area intuition meets the student with dx/dt and ∫v dt — and they turn out to be the same student.

Open the lessons →The formula reference The concept graph

Verification is the product

One build-time SymPy program solves each scenario two ways and proves the two agree, checks every formula is dimensionally sound, and exports a cheap closed form the browser evaluates for the interactive graphs. You are never told the registers agree — it is proven, and the proof is shown. Read how it is verified.