Pro 🔒~15 min

Force & Motion Graphs

Position-time, velocity-time, and acceleration-time graphs

How it works

A position-time graph shows where an object is. A straight line means constant velocity; a curve means acceleration. The slope of the x-t graph gives velocity. A velocity-time graph shows how fast the object moves. A horizontal line means constant velocity (no acceleration); a sloped line means constant acceleration. The slope of the v-t graph gives acceleration, and the area under it gives displacement. When net force is zero, velocity is constant. When friction opposes motion, the net force is F_applied - f_friction, and the object decelerates when the applied force is removed.

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Step-by-step

  1. Set the applied force, mass, and friction.
  2. Press Play to start the simulation.
  3. Watch the object move along a track while three graphs (x-t, v-t, a-t) update in real time.
  4. Change the force mid-simulation to see how graphs respond.

Key formulas

  • a=Fnetma = \frac{F_{\text{net}}}{m}Newton's 2nd law: net force divided by mass gives acceleration
  • v=v0+atv = v_0 + atVelocity changes linearly with constant acceleration
  • x=x0+v0t+12at2x = x_0 + v_0 t + \frac{1}{2}at^2Position is a quadratic function of time under constant acceleration

Frequently asked questions

A 5 kg object has a 5 N force applied with no friction. What is its acceleration?
A = F/m = 5/5 = 1 m/s².
What does a straight horizontal line on a velocity-time graph mean?
Constant velocity — the object moves at the same speed (acceleration is zero).