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College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300

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BuyFindarrow_forward

College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300
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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