Page 2: Time-Dependent Equations and Initial Conditions

This page delves into the mathematical formulation of motion equations and their initial conditions. It presents the complete set of equations for both position and velocity as functions of time.

Definition: Équation horaire represents the mathematical expression describing the position or velocity of an object as a function of time.

Highlight: Initial conditions are crucial for solving motion problems:

• At t = 0s: V(0) = Vo
• Position coordinates: x(0) = 0, y(0) = 0

Example: The complete time-dependent equations for position:

• x(t) = Vo cos(α)t
• y(t) = -½gt² + Vo sin(α)t

Vocabulary:

• Conditions initiales: Initial conditions
• Équations horaires: Time-dependent equations
• Position: Location in space
• Vitesse: Velocity

The page concludes with the full mathematical framework for analyzing projectile motion in a uniform field, incorporating both position and velocity equations with their respective initial conditions.