Understanding Motion

Kinematics explores how objects move, describing their position, velocity, and acceleration. In AP Physics C, calculus helps us analyze motion with greater precision.

Position, Velocity, and Acceleration

• Position (\(x\)) shows where an object is.
• Velocity (\(v\)) is the rate of change of position: \(v = \frac{dx}{dt}\).
• Acceleration (\(a\)) is the rate of change of velocity: \(a = \frac{dv}{dt}\).

With calculus, you can find velocity as the derivative of position, and acceleration as the derivative of velocity.

Motion in Two Dimensions

In two dimensions, motion is described with vectors. The position vector \(\vec{r}\) can be split into \(x\) and \(y\) components. Calculus helps analyze projectile motion and circular motion with changing velocities.

Graphical Analysis

Graphs of \(x\), \(v\), and \(a\) versus time are powerful tools for visualizing motion. The area under a velocity-time graph gives displacement.

Real-World Relevance

Whether analyzing a car's journey or a ball's flight, kinematics provides foundational tools to predict and understand motion.