Textbook Question
The speed v of an object is given by the equation v = At³ ― Bt, where t refers to time. What are the SI units for the constants A and B?
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1. Intro to Physics Units
Dimensional Analysis
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Join thousands of students who trust us to help them ace their exams!Watch the first videoMultiple Choice
Which of the following patterns is consistent with the principle of dimensional analysis?
A
The units on both sides of an equation must match.
B
The units of a derived quantity are always the same as its base quantities.
C
The numerical values on both sides of an equation must be equal.
D
The dimensions of a physical quantity can change with different unit systems.
Verified step by step guidance1
Dimensional analysis is a technique used to check the consistency of equations by comparing the dimensions of the physical quantities involved.
The principle of dimensional analysis states that for an equation to be valid, the dimensions on both sides must be the same. This ensures that the equation is physically meaningful.
Units are a representation of dimensions, and for an equation to be correct, the units on both sides must match. This is because units are derived from the dimensions of the physical quantities.
The numerical values on both sides of an equation do not necessarily have to be equal; rather, it is the dimensions that must be consistent.
Different unit systems can represent the same dimensions differently, but the fundamental dimensions (such as length, time, mass) remain unchanged. Therefore, the dimensions of a physical quantity do not change with different unit systems.
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