AP Physics 1 - Fundamental Concepts

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Scalar vs. Vector Quantities

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Scalars are physical quantities fully described by a magnitude (or numerical value) alone. Vectors are fully described by both a magnitude and a direction. Examples of scalars include speed and mass; examples of vectors include velocity and force.

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Displacement

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Displacement is a vector quantity that refers to the change in position of an object. It is calculated as the difference between the final position and the initial position ($\Delta x = x_f - x_i$). Unlike distance, displacement includes direction.

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Velocity vs. Speed

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Speed is a scalar describing how fast an object moves (distance/time). Velocity is a vector describing the rate of change of displacement (displacement/time). Velocity specifies direction, while speed does not. Formula: $\bar{v} = \Delta x / \Delta t$.

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Acceleration

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Acceleration is a vector quantity defined as the rate of change of velocity over time. An object accelerates if its speed changes, its direction changes, or both. Formula: $\bar{a} = \Delta v / \Delta t$. The SI unit is meters per second squared ($m/s^2$).

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Newton's First Law (Inertia)

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An object at rest stays at rest, and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced external force. This tendency to resist changes in motion is called inertia.