The v-t graphs of two moving objects make ang | vedclass

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Question

(A) The slope of a $v-t$ graph represents the acceleration of the object.Slope $a = 	an 	heta$,where $	heta$ is the angle made with the time axis.G

Vedclass · Accepted Answer

$1 : \sqrt{3}$

Vedclass · Answer

(A) The slope of a $v-t$ graph represents the acceleration of the object.Slope $a = 	an 	heta$,where $	heta$ is the angle made with the time axis.Given $	heta_{1} = 30^{\circ}$ and $	heta_{2} = 45^{\circ}$.The ratio of their accelerations is $\frac{a_{1}}{a_{2}} = \frac{	an 	heta_{1}}{	an 	heta_{2}}$.Substituting the values: $\frac{a_{1}}{a_{2}} = \frac{	an 30^{\circ}}{	an 45^{\circ}}$.Since $	an 30^{\circ} = \frac{1}{\sqrt{3}}$ and $	an 45^{\circ} = 1$,we get $\frac{a_{1}}{a_{2}} = \frac{1/\sqrt{3}}{1} = \frac{1}{\sqrt{3}}$.Therefore,the ratio is $1 : \sqrt{3}$.

The $v-t$ graphs of two moving objects make angles of $30^{\circ}$ and $45^{\circ}$ with the time axis. Find the ratio of their accelerations.

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