Physics HL · Chapter 1: Kinematics
1.3 Graphs of Motion
Infer velocity and acceleration behavior from graph shape when equations for constant acceleration do not apply directly.
Estimated time: 20 minutes
From Position-Time Shape to Velocity-Time Shape
When the position-time graph is curved, velocity is changing. You can sketch velocity-time qualitatively by reading the tangent slope trend: where the position graph steepens upward, velocity increases; where it flattens, velocity approaches zero; where it tilts downward, velocity becomes negative.
From Velocity-Time Shape to Acceleration-Time Shape
Acceleration is the slope of the velocity-time graph. A rising velocity curve means positive acceleration, a falling velocity curve means negative acceleration, and a horizontal velocity segment means zero acceleration.
Use Slope and Area Together
For robust interpretation, use both slope and area. Slope gives the local rate (velocity or acceleration), while signed area gives accumulated change (displacement or velocity change). This dual view prevents common mistakes like reading speed from area or displacement from slope.
Simulation: Shape Matching Across s-t, v-t, and a-t
Switch velocity profiles and observe how area and slope control displacement and acceleration stories.
Motion Graph Lab
v(t)
4.00 m/s
Displacement from 0 to t
6.00 m
Velocity-time graph
Test Yourself
A velocity-time graph lies below the time axis from t = 2 s to t = 5 s. What must be true on that interval?