The distance $r$ from the origin of a particle moving in $x - y$ plane varies with time as $r = 2t$ and the angle made by the radius vector with positive $x$-axis is $ heta = 4t$. Here, $t$ is in second, $r$ in metre and $ heta$ in radian. The speed of the particle at $t = 1$ s is

Question

The distance $r$ from the origin of a particle moving in $x - y$ plane varies with time as $r = 2t$ and the angle made by the radius vector with positive $x$-axis is $	heta = 4t$. Here, $t$ is in second, $r$ in metre and $	heta$ in radian. The speed of the particle at $t = 1$ s is

Dr. Abubacker · Accepted Answer

(b) Here, $r = 2t,	heta = 4t$
$l = r	heta = (2t)(4t) = 8t^{2}$
$v = \frac{dl}{dt} = \frac{d}{dt}(8t)^{2} = 16t$
$= 16 	imes 1 = 16\ ms^{- 1}$

Q. The distance $r$ from the origin of a particle moving in $x - y$ plane varies with time as $r = 2t$ and the angle made by the radius vector with positive $x$-axis is $\theta = 4t$. Here, $t$ is in second, $r$ in metre and $\theta$ in radian. The speed of the particle at $t = 1$ s is

Explanation

Reviewed by Dr. Abubacker

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