Answered: Assume the equation x = At3 + Bt…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Question

Assume the equation x = At³ + Bt describes the motion of a particular object, with x having the dimension of length and t having the dimension of time. Determine the dimensions of the constants A and B. (Use the following as necessary: L and T, where L is the unit of length and T is the unit of time.)

Expert Solution

Step 1

x having dimension of length $[L]$

t having dimension of time $[T]$

By using dimensional analysis of given equation

$x = A t^{3} + B t$

consider dimension of A and B are

$[A] = [L^{n} T^{m}] [B] = [L^{a} T^{b}]$

hence in dimensional form

$[L^{1} T^{0}] = [L^{n} T^{m}] [T^{3}] + [L^{a} T^{b}] [T] [L^{1} T^{0}] = [L^{n} T^{m + 3}] + [L^{a} T^{b + 1}]$

on comparing the both side

$n = 1, m + 3 = 0 n = 1 a n d m = - 3$ $a = 1, b + 1 = 0 a = 1 a n d b = - 1$

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