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Variation of G Due to the Rotation of Earth

If x=at+bt2...

Question

If $x = a t + b t^{2}$ where $x$ is in meter and $t$ is in second. what are the units of $a$ and $b$ ?

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Solution

$x = a t + {b t}^{2}$
$a t = x = a = \frac{x}{t} = [\frac{L}{T}] = [{L T}^{- 1}]$
${b t}^{2} = x = a = \frac{x}{t^{2}} = [\frac{L}{T^{2}}] = [{L T}^{- 2}]$

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