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← Kinematics
1.3

Representing Motion

Motion is described through graphs, equations, and calculus relationships linking position, velocity, and acceleration over time.

Change10–15% of exam
All TopicsPrevious1.2Displacement, Velocity, and AccelerationNext1.4Reference Frames and Relative Motion
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Context

What this topic is and why it exists

Imagine filming a ball tossed straight up and then scrubbing through the video frame by frame.
In the first few frames the ball climbs quickly—the gaps between its positions are large.
Near the top, the gaps shrink to almost nothing.
Then they widen again as the ball falls back down.
That single mental movie contains everything you need to know about representing motion: position tells you *where* the ball is, velocity tells you *how fast and which way* it's moving between frames, and acceleration tells you how that velocity itself is changing.
On Earth, gravity quietly tugs downward at about 10 m/s2s^{2}s2 the entire time—even at the very top, where the ball briefly stops.
Now translate that movie into math.
Velocity is the slope of a position-vs-time graph at any instant—literally the derivative, vₓ = dxdt\frac{dx}{dt}dtdx​.
Acceleration is the slope of the velocity graph, aₓ = dvₓ/dt.
When acceleration is constant, three tidy equations—vₓ = vₓ₀ + aₓt, x = x0x_{0}x0​ + vₓ₀t + ½aₓt2t^{2}t2, and vₓ² = vₓ₀² + 2aₓ(x − x0x_{0}x0​)—let you connect any combination of position, velocity, acceleration, and time.
Master moving fluidly between the picture, the graph, the equation, and the story in words, and you'll own kinematics problems rather than just survive them.
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