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A particle of mass m is acted upon by a force F given by the empirical law $F = \frac{R}{t^{2}} v (t)$ . If this law is to be tested experimentally by observing the motion starting from rest, the best way is to plot:

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$\log v (t) a g a i n s t \frac{1}{t}$

$\log v (t) a g a i n s t \frac{1}{t^{2}}$

$v (t) a g a i n s t t^{2}$

$\log v (t) a g a i n s t t$

answer is A.

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Detailed Solution

F = (R/t²)v(t)

$\Rightarrow m \frac{d v }{d t} = (\frac{R}{t^{2}}) v (t)$
$\Rightarrow \int v d v = \int (\frac{R}{m t^{2}}) d t$
ln v = −R/mt
⇒ ln v∝1/t

So, the plot of log v(t) against 1/t will be a straight line.

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