Position, Velocity and Acceleration Graphs

Slope down, area up

The three graphs are linked by two operations:

• Slope of a position graph gives velocity; slope of a velocity graph gives acceleration.
• Area under a velocity graph gives displacement; area under an acceleration graph gives change in velocity.

Signed area matters: area below the axis counts as negative.

Reading direction and speed correctly

The sign of $v$ tells you the direction of motion. The slope of the $v$-graph tells you whether the object speeds up or slows down — and only in combination: speeding up when $v$ and $a$ share a sign.

A velocity graph sloping downward while still above the axis describes an object moving forward and slowing, not moving backward.