Introducción al MRUV

Introduction to MRUV

• MRUV stands for Movimiento Rectilíneo Uniformemente Variado, meaning uniformly accelerated rectilinear motion.
• This type of motion is defined by a constant acceleration.
• The object's velocity changes at a consistent rate.

Key Characteristics of MRUV

• Constant Acceleration: The velocity change rate is constant.
• Rectilinear Motion: The motion follows a straight line.
• Variables: MRUV equations use displacement (x), initial velocity (v₀), final velocity (v), acceleration (a), and time (t).

Equations of Motion for MRUV

• These equations link MRUV variables, derived from calculus.
• Equation 1: v = v₀ + at (Velocity as a function of time)
  • Relates final velocity to initial velocity, acceleration, and elapsed time.
• Equation 2: x = v₀t + ½at² (Displacement as a function of time)
  • Shows displacement change over time, including initial velocity and acceleration.
• Equation 3: v² = v₀² + 2ax (Velocity squared as a function of displacement)
  • Relates final velocity squared to initial velocity squared, acceleration, and displacement. It's independent of time.

Specific Cases and Applications

• Free Fall: A common MRUV example, where acceleration is due to gravity (approximately 9.8 m/s² downward). Initial velocity is often zero in free fall scenarios.
• Projectiles: Projectile motion (like a thrown ball) can be analyzed using MRUV principles. Horizontal motion is frequently separated, but can be modeled with these equations.

Solving Problems Involving MRUV

• Problem-Solving Strategy:
  • Identify known variables.
  • Find the equation linking known and unknown variables.
  • Solve the equation for the unknown.
  • Substitute known values to find the unknown.
  • Ensure consistent units throughout calculations.

Graphs related to MRUV

• Velocity vs Time Graph: A straight line (constant positive or negative slope) represents uniformly accelerated motion. The slope shows the acceleration.
• Position vs Time Graph: A parabolic curve displays constant acceleration.

Considerations for Different Directions

• Positive and Negative Acceleration: Positive acceleration means the object speeds up in the direction of motion; negative (deceleration) means it slows down.
• Direction Matters: Maintain a consistent direction convention (usually positive or negative). Initial and final velocities must match the assigned direction.

Key Takeaways

• Understanding MRUV involves knowing the relevant equations and applying them to physical situations.
• Problem-solving is enhanced by a structured approach, identifying known and unknown variables correctly.
• Accurate results require careful attention to units and direction in calculations.