Position-time graph
Also called x-t graph, Position vs time graph
A position-time graph plots an object's position on the vertical axis against time on the horizontal. The slope at any point gives the velocity there, the curvature shows whether the object is accelerating, and the area underneath carries no physical meaning.
Read the steepness, not the height. Height says where the object is; steepness says how fast.
- Slope is velocity. EK 1.3.A.4.i: the instantaneous velocity is the slope of a line tangent to a point on a graph of position as a function of time. A flat stretch is an object at rest, a steeper line is a faster object, and a downward slope is motion in the negative direction.
- Curvature is acceleration. A straight line has an unchanging slope, so the velocity is constant. A curve means the velocity is changing. Curving upward is acceleration in the positive direction, curving downward is acceleration in the negative direction, whichever way the line happens to slope.
- There is no area reading. Every AP Physics 1 statement that gives an area a meaning starts from a velocity, acceleration, force or torque graph. Position times time is not a quantity the course uses.
The graph is not a picture of the path. A ball thrown straight up draws a parabola here while travelling along a vertical line through the air. A projectile launched at an angle does trace a parabola through space, but that one is a plot of against , not against time. Two different plots sharing a shape.
The graph can never double back on itself, since an object cannot be in two places at one time, and a turning point marks the instant it reverses.
The graph whose slope gives acceleration instead is the velocity-time graph; topic 1.3 Representing Motion carries the AP treatment of all three.