Simulation · Kinematics

One-dimensional kinematics

Explore position, velocity, and constant acceleration along an axis with synchronized graphs and a physical reading of changes in direction.

Physical model

One particle, one axis, constant acceleration

The simulation represents a particle on the x-axis over the interval 0 ≤ t ≤ T. Negative position describes one side of the origin; the sign of velocity describes the direction of motion.

x(t) = x₀ + v₀t + ½at²

v(t) = v₀ + at

a(t) = a

Motion along the x-axis

The circular marker shows the current position.

  • Start
  • Current position
Position axis in meters with the origin when it lies in the domain, the initial position, the current position, and an arrow indicating the positive x direction.x = -4 mx position (m) · +x

Synchronized readings

Physical state

Direction: toward +x

Instant t
0s
Position x
-4m
Displacement Δx
0m
Distance d
0m
Velocity v
6m/s
Speed |v|
6m/s
Acceleration a
-2m/s²

Predicted change of direction att = 3 s,x = 5 m.

Time

Playback

Paused

Graphs

Linked graphs

Three readings of the same motion

The curves show the full interval; the shared cursor marks the current instant.

x(t)

Its slope is velocity.

Complete graph of position against time. The vertical line and point indicate the simulation's current instant.

v(t)

Its slope is a; its signed area is Δx.

Complete graph of velocity against time. The vertical line and point indicate the simulation's current instant.

a(t)

Its signed area is the change in velocity.

Complete graph of acceleration against time. The vertical line and point indicate the simulation's current instant.

Exploration guide

What to observe

  1. 01

    Change only v₀ and compare the initial slope of x(t) with the initial value of v(t).

  2. 02

    Use “Slows down and returns”: when v crosses zero, x reaches an extreme and distance stops matching |Δx|.

  3. 03

    Compare the signs of v and a. Opposite signs reduce speed; equal signs increase it.

  4. 04

    Move the time control and verify that all three graphs mark exactly the same instant.

Scope

Model limits

Acceleration remains constant and the object is treated as a particle. The model does not include drag, collisions, forces, size, rotation, or discontinuous changes in acceleration. The animation illustrates the equations; it does not reproduce an experimental material or time scale.