Calculators/Physics/Kinematics calculator

Kinematics calculator

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

Kinematics calculator — illustration
Final velocity
10 m/s
Distance s
25 m
Average velocity
5 m/s
v(t) — velocity
t [s]
s(t) — distance
t [s]

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:

s=v⋅ts=v\cdot t

For uniformly accelerated motion (constant acceleration aa, initial velocity v0v_0):

v=v0+a ts=v0t+at22v2=v02+2asv=v_0+a\,t \qquad s=v_0 t+\frac{a t^2}{2} \qquad v^2=v_0^2+2as

Enter v0v_0, aa and tt — you will get the final velocity, the distance travelled and the average velocity, plus graphs of v(t)v(t) and s(t)s(t) (velocity grows linearly, distance along a parabola).

Examples

v₀ = 0, a = 2 m/s², t = 5 s
→ v = 10 m/s, s = 25 m, v_avg = 5 m/s
Uniform: v = 10 m/s, t = 8 s
→ s = 80 m

Frequently asked questions

How do you read distance off a v(t) graph?+

Distance is the area under the velocity graph. For uniformly accelerated motion it is the area of a trapezoid, hence s = v₀t + at²/2.

Why is s(t) a parabola?+

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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