{"id":235,"date":"2026-06-14T23:24:46","date_gmt":"2026-06-14T23:24:46","guid":{"rendered":"https:\/\/physicsfundamentalsinfo.com\/blog\/?p=235"},"modified":"2026-06-14T23:24:47","modified_gmt":"2026-06-14T23:24:47","slug":"motion-graphs","status":"publish","type":"post","link":"https:\/\/physicsfundamentalsinfo.com\/blog\/kinematics\/motion-graphs\/","title":{"rendered":"Motion Graphs in Physics"},"content":{"rendered":"\n
Definition<\/div>

\n\nMotion graphs are diagrams that plot an object’s position, velocity, or acceleration against time, showing exactly how its motion changes from moment to moment. The slope (gradient) of a position\u2013time graph gives velocity, the slope of a velocity\u2013time graph gives acceleration, and the area under a velocity\u2013time graph gives displacement.\n\n<\/p><\/div>\n

Pull out your phone after a run and look at the pace trace. That jagged line \u2014 climbing where you sped up, dipping where you walked \u2014 is a motion graph, and it tells the whole story of the run without a single row of numbers.<\/p>\n

Physics leans on these pictures constantly. One glance at the right graph reveals whether something is speeding up, slowing down, standing still or reversing \u2014 and, with a little slope and area, exactly how fast and how far. Learn to read them and the equations of motion suddenly make sense.<\/p>\n

What Are Motion Graphs?<\/h2>\n

Imagine describing a 20-minute drive without using any numbers. You might say “I sped up, cruised, braked at the lights, then crawled in traffic.” A motion graph turns that story into a precise line you can actually measure.<\/p>\n

Motion graphs are line graphs with time along the horizontal axis and one motion quantity \u2014 position, velocity, or acceleration \u2014 up the vertical axis. Each type answers a different question: where something is, how fast it is going, or how quickly its speed is changing.<\/p>\n

Time always runs along the bottom, because in everyday physics it only moves forward. The real physics lives on the vertical axis, and reading the line means reading two things at once: its height and its steepness.<\/p>\n

Distance\u2013time vs displacement\u2013time<\/h3>\n

One quick distinction trips up beginners. A distance\u2013time graph tracks the total ground covered, so its line can only rise or stay flat. A displacement\u2013time graph tracks position relative to a starting point, so it can fall back toward zero \u2014 or go negative \u2014 the moment you turn around.<\/p>\n

The difference mirrors the gap between speed and velocity: distance and speed ignore direction, while displacement and velocity respect it. For a full breakdown, see our guide on velocity vs speed<\/a>.<\/p>\n

The Three Types of Motion Graphs<\/h2>\n

Three graphs show up again and again, and they are linked like a chain. The slope of one becomes the graph below it.<\/p>\n

Displacement\u2013time (x\u2013t) graphs<\/h3>\n

Height shows position; steepness shows velocity. A flat line means the object sits still, a straight slope means steady velocity, and any curve means the velocity is changing.<\/p>\n

Velocity\u2013time (v\u2013t) graphs<\/h3>\n

Height shows velocity; steepness shows acceleration. Here a flat line no longer means “stopped” \u2014 it means constant velocity. The area trapped between the line and the time axis is the displacement.<\/p>\n

Acceleration\u2013time (a\u2013t) graphs<\/h3>\n

Height shows acceleration, and for most school problems this line is simply flat, meaning constant acceleration. The area underneath gives the change in velocity over that time interval.<\/p>\n

\n\n<\/marker><\/defs>\nHow the three motion graphs connect<\/text>\nAn object accelerating uniformly from rest<\/text>\n\n\nPosition (m)<\/text>\nt<\/text>\n\nslope = velocity (and it is increasing)<\/text>\n\n\n\nVelocity (m\/s)<\/text>\nt<\/text>\n\nslope = acceleration (constant)<\/text>\narea = displacement<\/text>\n\n\n\nAcceleration (m\/s\u00b2)<\/text>\nt<\/text>\n\nconstant value = flat line<\/text>\narea = change in velocity<\/text>\n<\/svg>\n<\/div>\n

The three graphs form a chain: take the slope<\/strong> to move down it (position \u2192 velocity \u2192 acceleration), and take the area<\/strong> to move back up (acceleration \u2192 velocity \u2192 position).<\/p>\n

\n\n\n\n\n\n\n\n
Graph type<\/th>\nSlope (gradient) gives<\/th>\nArea underneath gives<\/th>\nA flat horizontal line means<\/th>\n<\/tr>\n<\/thead>\n
Displacement\u2013time (x\u2013t)<\/strong><\/td>\nVelocity<\/td>\nNo standard physical meaning<\/td>\nObject is at rest (stationary)<\/td>\n<\/tr>\n
Velocity\u2013time (v\u2013t)<\/strong><\/td>\nAcceleration<\/td>\nDisplacement<\/td>\nConstant velocity (zero acceleration)<\/td>\n<\/tr>\n
Acceleration\u2013time (a\u2013t)<\/strong><\/td>\nJerk (rate of change of acceleration)<\/td>\nChange in velocity (\u0394v)<\/td>\nConstant acceleration<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n

Read the table across and a pattern jumps out: moving down the chain you take the slope, moving up the chain you take the area. That single idea unlocks almost every motion-graph question.<\/p>\n

The Motion Graph Formulas: Slope and Area<\/h2>\n

Two operations do all the heavy lifting \u2014 gradient and area. Everything else is just reading the axes carefully.<\/p>\n

v = \u0394x \/ \u0394t<\/div>\n

The gradient of a displacement\u2013time graph is the velocity.<\/p>\n

a = \u0394v \/ \u0394t<\/div>\n

The gradient of a velocity\u2013time graph is the acceleration \u2014 which, by Newton’s second law<\/a>, is exactly what a net force produces.<\/p>\n

s = area under the velocity\u2013time graph<\/div>\n
\u0394v = area under the acceleration\u2013time graph<\/div>\n

When a velocity\u2013time line is straight, that area is just a trapezium, which gives one of the standard equations of motion:<\/p>\n

s = \u00bd (u + v) t<\/div>\n

Here is what each symbol means, with its SI unit:<\/p>\n