Textbook Question
The position of a ball rolling in a straight line is given by 𝓍 = 2.0 ― 3.6t + 1.7t², where 𝓍 is in meters and t in seconds. What do the numbers 2.0, 3.6, and 1.7 refer to?
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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 pairs of physical quantities and their dimensions is mismatched?
A
Energy - [M L^2 T^-2]
B
Velocity - [M T^-1]
C
Pressure - [M L^-1 T^-2]
D
Force - [M L T^-2]
Verified step by step guidance1
Step 1: Understand the concept of dimensions in physics. Dimensions are a way to express the physical nature of a quantity in terms of basic quantities like mass (M), length (L), and time (T).
Step 2: Review the dimensional formula for each physical quantity given in the problem. For example, energy is typically expressed as [M L^2 T^-2], which corresponds to the formula for kinetic energy (1/2 mv^2) or potential energy (mgh).
Step 3: Analyze the dimensional formula for velocity. Velocity is defined as the rate of change of displacement with respect to time, which gives it the dimensional formula [L T^-1].
Step 4: Compare the given dimensional formula for velocity, [M T^-1], with the correct dimensional formula [L T^-1]. Notice that the given formula incorrectly includes mass (M), which is not a component of velocity's dimensions.
Step 5: Verify the dimensional formulas for the other quantities: Pressure is [M L^-1 T^-2], derived from force per unit area, and Force is [M L T^-2], derived from mass times acceleration. Both are correctly matched.
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