Movimiento Rectilíneo Uniformemente Acelerado o Variado MRUA MRUV | Ejemplo 2

Understanding Uniformly Accelerated Motion

Introduction to the Problem

• The video addresses the second problem of uniformly accelerated motion, encouraging viewers to practice by solving it themselves if they have watched previous videos in the course.

• Viewers are advised to review at least two prior videos: one explaining key concepts like speed and acceleration, and another detailing how to choose appropriate formulas for problems.

Identifying Given Data

• The instructor emphasizes writing down known data from the exercise, noting that three pieces of information are typically provided in these types of problems.

• An example is given where a car travels at an initial speed of 10 meters per second. It's crucial for students to recognize this as velocity even when not explicitly stated.

Understanding Acceleration and Time

• The car accelerates at a rate of 2 meters per second squared, which is identified as the acceleration.

• Although only two data points (initial velocity and acceleration) are initially presented, time (7 seconds) becomes relevant when answering questions about final velocity.

Formulating the Problem

• The first question asks for the car's speed after 7 seconds, introducing time as a new variable while space remains unknown.

• Students must identify which formula does not involve space since it is not provided; this helps narrow down options for calculations.

Choosing the Right Formula

• The instructor reviews various formulas to find one that excludes space. Only certain formulas can be used based on available data.

• A specific formula is selected that allows calculation of final velocity directly using known variables: initial velocity, acceleration, and time.

Calculation Process

• To ensure clarity during calculations, it's recommended to write down chosen formulas alongside their variables before proceeding with numerical substitutions.

• Emphasis is placed on maintaining consistent units throughout calculations—meters for distance and seconds for time—to avoid conversion errors later on.

Performing Calculations

• With all values confirmed in compatible units (meters and seconds), students can substitute into the formula: final velocity = initial velocity + (acceleration × time).

• After performing operations correctly—multiplying before adding—the final result shows that after 7 seconds, the car's speed reaches 24 meters per second.

Conclusion of Example Problem

Understanding Motion: Key Concepts and Calculations

Initial Velocity and Time Considerations

• The initial velocity is stated as 24 meters per second, applicable specifically at the 7-second mark. If a different time frame (e.g., 2 seconds) is given, this data cannot be used.

• When asked about distance traveled in 7 seconds, both the initial velocity and acceleration can be utilized since they correspond to that specific time.

Calculating Distance Traveled

• To find the distance traveled, all relevant data must be collected. The formula chosen should ideally have space (distance) isolated for easier calculation.

• Various formulas are considered; those with space clearly defined are preferred to simplify calculations.

Formula Selection and Application

• The selected formula must allow for straightforward substitution of known values. Preference is given to formulas where space is already solved for.

• A specific formula is copied down for clarity before substituting known values into it.

Performing Calculations

• Substituting values into the formula involves ensuring all units are consistent (meters and seconds).

• The calculation begins with multiplying initial velocity by time, followed by calculating acceleration's contribution over time squared.

Finalizing Results

• After performing necessary operations, results yield a total distance of 119 meters after combining contributions from both initial velocity and acceleration.

• It’s emphasized that final answers should include units (meters), reinforcing the importance of unit consistency throughout calculations.

Addressing Additional Questions on Time

• A new question arises regarding how long it takes to reach a speed of 18 meters per second. This requires careful consideration as previous data points may not apply.

• Since the earlier calculations were based on reaching speeds at 7 seconds, new parameters must be established without relying on prior distances or velocities acquired at that point.

Identifying Relevant Formulas for New Parameters

• For determining time taken to reach a new speed, it's crucial to identify formulas that do not require knowledge of distance since it remains unknown in this scenario.

Understanding Motion and Acceleration

Key Concepts in Motion Equations

• The speaker discusses the process of isolating time in motion equations, emphasizing that it can be done by rearranging terms. Multiplication and division are highlighted as key operations for solving these equations.

• The choice between two formulas is presented, with the speaker indicating a preference for whichever formula simplifies calculations. Both options should yield the same result if applied correctly.

• An example is provided where final velocity (18 m/s) is calculated using initial velocity (10 m/s), acceleration (2 m/s²), and an unknown time. A cautionary note is given about not mixing addition with multiplication in calculations.

• The calculation proceeds by isolating variables; here, 10 is subtracted from both sides to solve for time. The importance of maintaining correct units throughout the calculation process is emphasized.

• The final answer indicates that achieving a speed of 18 m/s takes 4 seconds, reinforcing the need to express answers clearly in words alongside numerical results.

Practice Exercise Introduction

• After explaining the concept, the speaker introduces a practice exercise for viewers to attempt on their own, encouraging them to pause and read through it carefully before attempting a solution.

Analyzing Deceleration

• A new scenario involves an object moving at an initial speed of 21 m/s which begins decelerating due to brakes being applied. This introduces negative acceleration (-3 m/s²).

• A correction regarding units is made; acceleration must be expressed as meters per second squared (m/s²). This highlights common mistakes when dealing with physical quantities.

• The speaker explains that sometimes problems will refer to "deceleration" instead of providing direct values for acceleration, which requires understanding how to apply negative signs appropriately.

Calculating Final Velocity After Time Interval

• Given known values (initial speed and negative acceleration), viewers are tasked with finding final velocity after 5 seconds without needing distance information.

• Two potential formulas are identified for calculating final velocity; however, one must ensure they do not include distance since it's unknown in this case.

Detailed Calculation Steps

• The chosen formula incorporates initial speed and negative acceleration over time. Units are checked for consistency before performing calculations.

• As calculations proceed, care is taken to maintain clarity around signs during operations involving addition or subtraction of velocities influenced by acceleration.

Physics Problem Solving: Understanding Motion

Choosing the Right Equation

• When faced with multiple equations for motion, any can be used if none fit perfectly. The speaker chose the first equation for this problem.

Rearranging Equations

• To isolate time in the equation, the speaker emphasizes that dividing by a number (in this case, negative acceleration) requires careful attention to signs.

Handling Negative Values

• A common mistake among students is changing the sign when dividing by a negative. The speaker suggests removing negatives by multiplying through by -1 to simplify calculations.

Calculating Time

• After adjusting signs, the calculation leads to finding time as 7 seconds using straightforward division of initial velocity and acceleration.

Finding Distance Traveled

• With final velocity at zero, all necessary data points are available to calculate distance. The formula used involves initial velocity and time squared.

Performing Calculations

• The distance formula incorporates both initial velocity and acceleration over time squared. This results in a calculated distance of 73.5 meters after performing necessary arithmetic operations.

Encouragement for Further Learning