Question 136: Laws of Motion

Question

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

Accepted Answer

Given,
F = $${R \over {{t^2}}}$$ v(t)
$$ \Rightarrow $$   m $${{dv} \over {dt}}$$   =  $${R \over {{t^2}}}$$ (v)
$$ \Rightarrow $$   $${{dv} \over v}$$ = $${R \over m}$$ $${{dt} \over {{t^2}}}$$
Intergrating both sides,
$$\int {{{dv} \over v} = {R \over m}\int {{{dt} \over {{t^2}}}} } $$
$$ \Rightarrow $$   lnv = $${{R \over m}}$$ $$ 	imes $$ $$\left( { - {1 \over t}} ight)$$ + C
$$ \Rightarrow $$   lnv = $$-$$ $${{R \over m}}$$ $$\left( {{1 \over t}} ight)$$ + C
Graph between lnv and $${{1 \over t}}$$ will be straight line curve.

Answer

$$\upsilon $$(t) against t2

Answer

log $$\upsilon $$(t) against $${1 \over {{t^2}}}$$

Answer

log $$\upsilon $$(t) against t

Answer

log $$\upsilon $$(t) against $${1 \over {{t}}}$$

Laws of Motion

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

Choose the correct answer: