Kinematics · 22 min
Graphical Analysis of Motion
Slope, area, and curvature — a graph is three answers in one picture.
Why should I care?
Without knowing any equation, could you find how far a car travelled just by looking at its velocity-time graph?
Yes — the area under a velocity-time graph is displacement. This is one of the most useful facts in kinematics, and it works whether the motion is steady or constantly changing.
Explore
Three graphs, one motion
Move the slider and watch position, velocity, and acceleration graphs update together — a steeper position graph always produces a higher point on the velocity graph, and so on down the chain.
The idea
Slope and area carry meaning
On a position-time graph, the slope is velocity. On a velocity-time graph, the slope is acceleration, and the area under the curve is displacement. Reading these three graphs together tells the complete story of a motion.
True or false?
A steeper velocity-time graph always means a greater displacement.
Worked example
Worked example
A velocity-time graph shows constant velocity of 8 m/s for 6 s. Find the displacement using the graph.
- 1
The area under a constant velocity line is a rectangle.
Your turn
On a velocity-time graph, what does the area under the curve represent?