Graphical analysis of motion

Reading the curves

• (position–time) curve: the slope of the tangent gives the velocity; a point with a horizontal tangent is an instant of zero velocity.
• (velocity–time) curve: the slope of the tangent gives the acceleration, and the area under the curve gives the displacement.
• If the velocity graph is a straight (inclined) line the acceleration is constant; if it is a horizontal line the velocity is uniform and the acceleration is zero.
• Area above the time axis is positive displacement, area below it is negative displacement; to get distance add the areas with their absolute values.
• The intersection of two (velocity–time) curves marks the instant when the two bodies have equal velocities — not necessarily when they meet.