Key Concepts: Graphical Analysis of Motion

Position-Time (x-t) Graphs

• Slope = velocity. A steeper slope means faster motion.
• Straight line = constant velocity. Curved line = changing velocity (acceleration).
• Horizontal line = object at rest.

Velocity-Time (v-t) Graphs

• Slope = acceleration. Positive slope = speeding up; negative slope = slowing down.
• Area under the curve = displacement. Area above the time axis is positive; below is negative.
• Horizontal line = constant velocity (zero acceleration).

Acceleration-Time (a-t) Graphs

• Area under the curve = change in velocity (Δv).
• Horizontal line = constant (uniform) acceleration.

Converting Between Graphs

• Differentiate x-t → v-t → a-t (take slopes).
• Integrate a-t → v-t → x-t (take areas).