The displacement of an object moving under uniform acceleration is some function of time and the acceleration. Suppose we write this displacement as s = kamtn, where k is a dimensionless constant. Show by dimensional analysis that this expression is satisfied if m = 1 and n = 2. Can the analysis give the value of k?

University Physics Volume 1
18th Edition
ISBN:9781938168277
Author:William Moebs, Samuel J. Ling, Jeff Sanny
Publisher:William Moebs, Samuel J. Ling, Jeff Sanny
Chapter1: Units And Measurement
Section: Chapter Questions
Problem 52P: Consider the physical quantities m,s,v,a, and t with dimensions [m]=M,[s]=L,[v]=LT1 and [a]=LT2 ....
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The displacement of an object moving under uniform acceleration is some function of time and the acceleration. Suppose we write this displacement as s = kamtn, where k is a dimensionless constant. Show by dimensional analysis that this expression is satisfied if m = 1 and n = 2. Can the analysis give the value of k?

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