Continuación: Movimiento Rectílineo Uniformemente Variado.

Summary

The video explains how to solve a physics problem involving an object's motion with acceleration. It covers two key questions: how long it takes for the object to stop and how long it takes to reach a specific point. Using equations of motion, the video demonstrates that the object takes 2 seconds to come to a stop and 6 seconds to reach a target 6 meters away. The process involves applying kinematic formulas, solving quadratic equations, and understanding the relationships between initial velocity, acceleration, and time.

Takeaways

• 😀 The goal of the problem is to calculate the time it takes for an object to stop, given its initial velocity, final velocity, and acceleration.
• 😀 To find the stopping time, the acceleration is isolated in the equation, and the time is calculated by substituting known values.
• 😀 The final velocity is zero (since the object comes to a stop), and the initial velocity is -2 m/s.
• 😀 The acceleration is given as 1 m/s², leading to a result that the object stops in 2 seconds.
• 😀 The second part of the problem involves finding how long it takes for the object to travel a certain distance (6 meters).
• 😀 The initial position is 0 meters, and the initial velocity is -2 m/s.
• 😀 The equation for uniformly accelerated motion is used to solve for the time to reach 6 meters, involving the quadratic formula.
• 😀 The quadratic equation provides two possible time solutions, one positive and one negative. The negative time is discarded.
• 😀 The positive solution is 6 seconds, meaning it takes the object 6 seconds to reach the 6-meter mark.
• 😀 The results are verified with a graph, confirming that the object takes 2 seconds to stop and 6 seconds to reach 6 meters.
• 😀 The entire process demonstrates the application of kinematic equations to solve for time and distance in motion problems.

Q & A

What is the initial velocity of the object in the script?

The initial velocity of the object is -2 m/s, indicating it is moving in the negative direction.

What is the deceleration of the object, and how does it affect its motion?

The deceleration is 1 m/s², which means the object is slowing down at a rate of 1 meter per second squared until it eventually stops.

How do you calculate the time it takes for the object to stop?

To calculate the time it takes for the object to stop, the equation v_f = v_i + at is used, where the final velocity (v_f) is 0, the initial velocity (v_i) is -2 m/s, and the acceleration (a) is -1 m/s². Solving for time gives 2 seconds.

What mistake could someone make when calculating the time to stop, and how can it be avoided?

A common mistake could be incorrectly handling the negative signs when substituting values. It can be avoided by correctly maintaining the negative sign for both the velocity and acceleration, as demonstrated in the equation.

What does the equation x = x_0 + v_i t + ½ a t² represent in this context?

This equation is used to determine the position of the object over time, considering its initial position, velocity, and acceleration. In this context, it calculates how long it takes for the object to reach the position of Yesi, located 6 meters away.

How is the quadratic equation derived in the script?

The quadratic equation is derived by substituting known values into the kinematic equation x = x_0 + v_i t + ½ a t², with x = 6 meters, x_0 = 0, v_i = -2 m/s, and a = 1 m/s², resulting in a simplified quadratic equation.

What is the solution to the quadratic equation for the time to catch Yesi?

The quadratic equation yields two possible solutions for time: t1 = 6 seconds and t2 = -2 seconds. The negative solution is discarded because time cannot be negative, leaving the valid solution of 6 seconds.

How does the negative solution in the quadratic equation affect the final result?

The negative solution in the quadratic equation corresponds to a time before the starting point, which is not physically meaningful in this scenario. Therefore, it is discarded, and only the positive solution (6 seconds) is taken as the valid answer.

What role does the acceleration play in this problem?

The acceleration determines how quickly the object slows down or speeds up. In this case, the negative acceleration (deceleration) causes the object to eventually stop, while the positive acceleration would speed it up if it were moving in the opposite direction.

How is this problem related to motion in physics?

This problem is a classic example of kinematic equations in physics, where the motion of an object is analyzed using its initial velocity, acceleration, and time to calculate key parameters such as time to stop or the time to reach a specific position.