The position of an object is given by 𝓍 = At + Bt², where 𝓍 is in meters and t is in seconds. What are the units of A and B?

Verified step by step guidance

1. Step 1: Start by analyzing the given equation for position: 𝓍 = At + Bt². Here, 𝓍 represents position in meters (m), t represents time in seconds (s), and A and B are constants with unknown units.
2. Step 2: Focus on the term At. Since 𝓍 is in meters, the product At must also have units of meters. The unit of t is seconds (s), so the unit of A must be meters per second (m/s) to ensure the product At has units of meters.
3. Step 3: Now, consider the term Bt². Again, since 𝓍 is in meters, the product Bt² must also have units of meters. The unit of t² is seconds squared (s²), so the unit of B must be meters per second squared (m/s²) to ensure the product Bt² has units of meters.
4. Step 4: Summarize the findings: The unit of A is meters per second (m/s), and the unit of B is meters per second squared (m/s²).
5. Step 5: Verify the consistency of units in the equation: Substitute the derived units of A and B into the equation 𝓍 = At + Bt². Confirm that both terms At and Bt² have units of meters, ensuring the equation is dimensionally consistent.

Key Concepts

Kinematic Equations

Kinematic equations describe the motion of objects under constant acceleration. In this context, the equation 𝓍 = At + Bt² represents the position of an object as a function of time, where A and B are coefficients that influence the object's motion. Understanding these equations is essential for analyzing how position changes with time.

Dimensional Analysis

Dimensional analysis is a method used to convert units and check the consistency of equations. By analyzing the dimensions of each term in the equation, we can determine the units of A and B. This technique ensures that all terms in the equation are compatible, which is crucial for solving physics problems.

Units of Measurement

Units of measurement provide a standard for quantifying physical quantities. In this equation, 𝓍 is measured in meters (m) and time t in seconds (s). The units of A and B can be derived from the equation by ensuring that the terms on both sides have the same dimensions, leading to a clear understanding of their physical significance.