Summary of "Função posição e equações do MRUV (exercícios)"

The video discusses exercises related to the concepts of position function and equations of uniformly accelerated motion (MRUV). The speaker walks through two problems involving cars in motion, applying relevant equations and methodologies to calculate distances, speeds, and the time at which one car overtakes another.

Main Ideas and Concepts

Understanding MRUV: The speaker emphasizes the importance of understanding uniformly accelerated motion, where the acceleration is constant.
Reference Frames: The choice of reference frames is crucial for solving problems. The speaker defines a reference to simplify calculations.
Equations of Motion: The speaker uses specific Equations of Motion to derive unknown variables such as distance, speed, and acceleration.

Methodology and Instructions

Problem 1: Car Braking

Given: A car moving at 108 km/h (converted to 30 m/s) stops in 3 seconds.
Steps:
- Draw a diagram to visualize the problem.
- Identify initial velocity (30 m/s), final velocity (0 m/s), and time (3 seconds).
- Use the equation v_f = v_0 + a • t to find acceleration:
  - 0 = 30 + a • 3 leads to a = -10 m/s².
- Use the equation for displacement: Δx = v_0 • t + ½ a t² to find distance:
  - Δx = 30 • 3 + ½ (-10) • (3²) = 90 - 45 = 45 m.

Problem 2: Two Cars in Motion

Given: Car A starts from rest with an acceleration of 4 m/s² and is initially 100 meters behind Car B, which moves at 10 m/s.
Steps:
- Define position functions for both cars:
  - Car B: x_B = 100 + 10t
  - Car A: x_A = 0 + 0 + ½ (4)t² = 2t²
- Set the equations equal to find when they meet: 2t² = 100 + 10t leads to 2t² - 10t - 100 = 0.
- Use the Quadratic Formula to solve for t: t = &frac{-b ± &sqrt{b² - 4ac}}{2a} results in t = 10 seconds (the physically acceptable solution).

Conclusion

The speaker concludes that Car A will overtake Car B after 10 seconds. The video emphasizes the importance of properly defining the reference frame and accurately applying Equations of Motion to solve problems in Physics.