Motion graphs turn a journey into two pictures — position against time and velocity against time — whose slopes carry the physics. Drag the sliders below to set the initial velocity and acceleration, press play, and watch both graphs draw in real time.
One journey, two graphs, two very different-looking stories. Set the Initial velocity u and the Acceleration a, press Play, and the dot slides along its track while the position-time and velocity-time graphs draw side by side. The pictures look nothing alike, yet they describe the exact same motion. What ties them together is one idea: the slope of each graph hands you the next quantity down.
On the position-time graph, the slope at any instant is the velocity. Give the dot a steady a and that curve bends into a parabola, because its steepness keeps growing as the dot speeds up. A straight, sloped position line would instead mean constant velocity and zero acceleration. On the velocity-time graph the slope is the acceleration, so a constant a draws a straight sloped line, and the area beneath it equals the displacement, following s = u·t + ½·a·t². Here is the trap: read the slope, never the height. A tall point on one graph is not the value on the other.
Watch how a curved position-time graph and a straight velocity line report the same run of v = u + a·t. Nudge a (in m/s²) toward zero and the velocity-time line flattens to horizontal while the position-time graph straightens into a sloped line — a reminder that a straight, tilted position graph still means steady motion. To rebuild the acceleration behind these slopes, open the acceleration lab, or step through every term in the SUVAT lab. Then pin down the exact numbers with the acceleration calculator and browse the full collection of physics sims.
The velocity. A steeper slope means a faster speed, and a horizontal line means the object is at rest. Under constant acceleration the position-time graph is a curved parabola.
The acceleration. A constant acceleration gives a straight sloped line; a horizontal line means constant velocity, which is zero acceleration.
It is the area between the line and the time axis. Area below the axis (negative velocity) counts as displacement in the opposite direction.
Because position follows s = u·t + ½·a·t², which is quadratic in time — a parabola. The velocity (the slope) keeps changing, so the curve steepens.