Mechanics · Physics

Motion Graphs & Equations of Motion Simulation

Drive a car through a journey and watch its x–t, v–t and a–t graphs draw themselves from the same motion. Read velocity as the slope of x–t and displacement as the area under v–t, build your own journey, and test v = u + at and s = ut + ½at².

Interactive virtual lab · no download · works on phones and laptops

Chapter: Kinematics
For: Class 9 · Class 11 · JEE · NEET
Time: ~15 min

How to use it

1Pick a journey (or build your own from segments) and press play.
2Drag the time slider; the tangent and shaded area follow.
3Equations of motion: set u, a and t and check the three equations.

What to notice

The slope of x–t is the velocity; the slope of v–t is the acceleration.
The signed area under v–t is the displacement; distance counts the parts below the axis as positive.
At a turning point x–t peaks and v crosses zero, but a need not be zero.
v = u + at and s = ut + ½at² hold only while a is constant.

For teachers

Teach it in 22 minutes

A lesson plan, questions to put to the class, a quick quiz you can project or print, and the formulas behind Motion Graphs & Equations of Motion.

1Hook
~2 min
- Play a journey with the graphs hidden and ask the class to sketch the x–t graph on paper. Then reveal it.
2Demonstrate
~9 min
- Pick a journey (or build your own from segments) and press play.
- Drag the time slider; the tangent and shaded area follow.
- Equations of motion: set u, a and t and check the three equations.
3Pause and ask
~5 min
- Have a student say this in their own words: The slope of x–t is the velocity; the slope of v–t is the acceleration.
- Have a student say this in their own words: The signed area under v–t is the displacement; distance counts the parts below the axis as positive.
- Have a student say this in their own words: At a turning point x–t peaks and v crosses zero, but a need not be zero.
- Have a student say this in their own words: v = u + at and s = ut + ½at² hold only while a is constant.
4Check
~6 min
- Run the 6-question quiz below: project it and take answers by show of fingers (1–4), or print it as a worksheet.

About the Motion Graphs & Equations of Motion simulation

Motion along a straight line is described by three graphs: position against time (x–t), velocity against time (v–t) and acceleration against time (a–t). They are tied together: the slope of x–t is the velocity, the slope of v–t is the acceleration, and the signed area under v–t is the displacement. Reading one graph from another is one of the most tested skills in kinematics.

This motion graphs simulation drives a car through a journey — at rest, uniform motion, speeding up, braking, turning back, a bus trip between stops, or one you build from segments — and draws all three graphs from the same motion as it goes. A tangent on x–t shows the velocity at any instant and a shaded area under v–t shows the displacement so far. The second tab checks the equations of motion for constant acceleration, including the difference between distance and displacement when the car reverses.

Also covers: position time graph, velocity time graph, acceleration time graph, x-t graph, v-t graph, slope of graph, area under v-t graph, distance vs displacement, uniform motion, equations of motion, suvat, average velocity, average speed, non uniform acceleration.

Frequently asked questions

What does the slope of a position–time graph represent?

The velocity. A straight x–t line means constant velocity; a curve means the velocity is changing; a flat line means the body is at rest.

How do you find displacement from a velocity–time graph?

Find the area between the graph and the time axis: area above the axis counts positive, below it negative. Adding all the parts as positive gives the distance travelled instead.