Uniform and accelerated motion · v(t), s(t) graphs

v = v₀ + a·t, s = v₀·t + a·t²/2, v² = v₀² + 2a·s (v(t) linear, s(t) parabola)
A calculator for rectilinear motion. For uniform motion (constant velocity) the distance is simply:
For uniformly accelerated motion (constant acceleration , initial velocity ):
Enter , and — you will get the final velocity, the distance travelled and the average velocity, plus graphs of and (velocity grows linearly, distance along a parabola).
Distance is the area under the velocity graph. For uniformly accelerated motion it is the area of a trapezoid, hence s = v₀t + at²/2.
Because distance depends on the square of time (the at²/2 term). In uniform motion (a = 0) only the linear term remains and the s(t) graph is a straight line.
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