Velocity is related to acceleration and distance by the following expression: v2 = 2axp

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1

Velocity is related to acceleration and distance by the following expression: v2 = 2axp. Find the power p that makes this equation diniensionally consistent.

Answer:

The equation will be consistent only when the dimensional formulae of all the terms on left side of the equation must be same as the dimensional formulae of all the terms on right side.
The dimensional formula of length is [L].
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The given expression is,
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The equation will be consistent only when p+1 = 2.
p+1 = 2.
p = 2
Therefore, the equation will be consistent when the power p is 1.

2

Why are the exponents negative and what happened to the initial 2 in from of acceleration?

3

the exponent for T is negative because the original expression is L/T , so T comes up with its exponent in negative form.