### Physics Problem: Unit Analysis and Dimensional Consistency#### 1. Problem Statement**Equation 1:**\[ 12.2 \, \frac{\text{kg} \cdot \text{m}^2}{\text{s}^2} = \frac{1}{2} \cdot x \cdot (5.2 \, \text{m/s})^2 \]- **Instruction:** Identify the units of \( x \) and explain your reasoning based on specific physics rules.- **Completion:** \( x \) has units of __________ because of Rule # _______.#### 2. Linear Motion Equation**Equation 2:**\[ y = (94.1 \, \frac{\text{m}}{\text{s}})(0.18 \, \text{s}) + x \]- **Instruction:** Determine the units of \( x \) and justify your answer by referring to the pertinent physics principles.- **Completion:** \( x \) has units of __________ because of Rule # _______.### Notes:- **Equation 1:** The left-hand side is expressed in units of energy (Joules), which is \( \text{kg} \cdot \text{m}^2/\text{s}^2 \). On the right-hand side, the term involving \( x \) includes a squared velocity term, requiring dimensional balancing to solve for \( x \).- **Equation 2:** A linear equation representing physical displacement combines speed and time to determine \( y \), thus influencing the dimensional analysis for \( x \).### ObjectiveUnderstand how to maintain consistency in units through proper application of dimensional analysis, ensuring each equation's coherence by correctly identifying unit specifications for unspecified variables. **Determine the Units of the Variable**In each of the following equations, determine the units of the variable \( x \) and specify which rule you used to determine this. Do not solve for the numeric value of \( x \). Show your work beneath the question, or on a separate sheet of paper.---**Rules:**- **Rule #1:** Both sides of the equal sign must have the same units.- **Rule #2:** Values that are added or subtracted must have the same units.- **Rule #3:** Argument of a trigonometric function must be an angle.- **Rule #4:** Argument of an inverse trig function must have no units.- **Rule #5:** Exponents must have no units.---**Example:**\[ 315 \text{ feet} = \frac{1}{2} \left(32 \frac{\text{feet}}{\text{s}^2}\right) x^2 \]\( x \) has units of **seconds** because of Rule #1.

Determine the units of the variable x in each of the following equations, and specify which rule you used to determine this. Do not solve for the numeric value of x. Show your work beneath the question, or on a separate sheet of paper. Example: 315 feet (32)x² = Rule #1: Both sides of the equal sign must have the same units. Rule #12: Values that are added or subtracted must have the same units. Rule #3: Argument of a trig function must be an angle. Rule #14: Argument of an inverse trig function must have no units. Rule #5: Exponents must have no units. x has units of seconds because of Rule # 1

Determine the units of the variable x in each of the following equations, and specify which rule you used to determine this. Do not solve for the numeric value of x. Show your work beneath the question, or on a separate sheet of paper. Example: 315 feet (32)x² = Rule #1: Both sides of the equal sign must have the same units. Rule #12: Values that are added or subtracted must have the same units. Rule #3: Argument of a trig function must be an angle. Rule #14: Argument of an inverse trig function must have no units. Rule #5: Exponents must have no units. x has units of seconds because of Rule # 1

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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