   Chapter 1, Problem 73AP

Chapter
Section
Textbook Problem

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?

To determine
The m=1 and n=2 by dimension analysis by using the equation of displacement.

Explanation

Given Info: The equation of the displacement is s=kamtn .

Explanation:

The dimension of displacement is,

[s]=[L]

The dimension of acceleration is,

[a]=[LT2]

The dimension of time is,

[t]=[T]

In the equation, the term (k) is constant, so it is dimensionless.

Calculating the dimension of the both side of the given equation,

[L]=[LT-2]m[T]n

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