Solve uniform motion, constant acceleration, Torricelli, free fall, vertical, horizontal and oblique launches: fill in what you know, leave blank what you want, and see the chosen equation, the substitution with units and the graphs.
Kinematics describes motion without asking about forces. This calculator always works in SI inside (metre, second, m/s and m/s²) and accepts km/h, min, cm, mi/h and more outside, showing each conversion, such as 72 km/h ÷ 3.6 = 20 m/s. In uniform motion the velocity is constant and Δs = v·t. With constant acceleration three equations solve everything: v = v₀ + a·t, Δs = v₀·t + a·t²/2 and Torricelli's v² = v₀² + 2·a·Δs, which does not need the time. There are five quantities (Δs, v₀, v, a, t) and two independent equations, so three known values fix the other two. The tool picks the equation that does not contain the variable you did not give, and says so. When the algebra ends in a square root there are two mathematical answers, and only those with non-negative time are kept: with v₀ = 20 m/s and a = -10 m/s², the body is at Δs = 15 m at t = 1 s (going up) and at t = 3 s (coming down). Data that contradict each other, are not enough, or demand a negative time are flagged instead of producing a meaningless number. In free fall and vertical launches the acceleration is g, which you choose: 10 m/s² for exercises, 9.8 m/s² for school, 9.80665 m/s² (the standard value, exact by definition) or the Moon (1.62 m/s²) and Mars (3.73 m/s²) values from the NASA fact sheets. In horizontal and oblique launches the axes are independent: uniform horizontally (x = v₀·cosθ·t) and uniformly accelerated vertically (y = h₀ + v₀·sinθ·t - g·t²/2). With h₀ = 0 the range is v₀²·sin2θ/g, the maximum height is v₀²·sin²θ/(2g) and the maximum range happens at 45°; launching from a height h₀ > 0, the best angle falls below 45°. All of this assumes a vacuum: with air drag the real range is shorter and the best angle also drops. Average speed is total distance divided by total time, which is why 60 km at 60 km/h plus 60 km at 120 km/h gives 80 km/h, not 90 km/h.
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In uniform motion the velocity does not change (zero acceleration) and position grows along a straight line on the s-t graph: S = S₀ + v·t. With constant acceleration the acceleration is non-zero, velocity changes linearly, v = v₀ + a·t, and the s-t graph is a parabola: S = S₀ + v₀·t + a·t²/2. Uniform motion is the special case with a = 0. A car at a steady 72 km/h covers 100 m in 5 s; one starting from rest with a = 2 m/s² covers 25 m in the same 5 s.
Uniform motion
Constant acceleration
Free fall and vertical
Horizontal launch
Oblique launch
Average speed
Units
= 100 m
Leave blank what you want to find. Three values are enough for constant acceleration, two for uniform motion.
Δs = v·t
Δs = v·t
Δs = 20·5 = 100
Δs = 100 mThe slope of the curve at each point is the velocity at that instant.
Area under the curve (signed) = displacement Δs = 100 m.
Area under the curve = change in velocity Δv = 0 m/s.