Representing motion

Motion in one dimension can be represented through motion diagrams, figures, graphs, equations, and narrative descriptions. When acceleration is constant, three kinematic equations relate position, velocity, acceleration, and time. Each equation connects four of the five kinematic variables, so the choice of equation depends on which quantity is known and which is sought.

v = v₀ + at x = x₀ + v₀t + ½at² v² = v₀² + 2a(x − x₀)

Free-Fall Acceleration

• Near Earth's surface, free-fall acceleration is approximately constant at 9.8 m/s² directed downward (often approximated as 10 m/s²)
• The same kinematic equations apply in the vertical direction, with $a_{\mathrm{y}}$ = ±g depending on the chosen sign convention

Graphs of Position, Velocity, and Acceleration Versus Time

Graphs of position, velocity, and acceleration versus time are connected through slopes and areas.

• The slope of a position–time graph gives instantaneous velocity
• The slope of a velocity–time graph gives instantaneous acceleration
• The area under a velocity–time graph gives displacement
• The area under an acceleration–time graph gives the change in velocity

Mastering the ability to translate between these representations — diagrams, graphs, equations, and words — is essential, because AP FRQs routinely require students to extract information from one form and express it in another.