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JEE Main 20199 JanuaryEvening Shift

Exam: JEE Main
Year: 2019
Date: 9 January
Shift: Evening Shift
Subject: Physics
Chapter: Mathematics in Physics

JEE Main 2019 · 9 January · Evening Shift · Physics · Mathematics in Physics

The position co-ordinates of a particle moving in a 3D coordinate...

The position co-ordinates of a particle moving in a

3D

coordinate system is given by

x = acos \omegat

y = asin \omegat

and

z = a\omegat

The speed of the particle is:

Options

A $\sqrt{2}a\omega$
B $a\omega$
C $2a\omega$
D $\sqrt{3}a\omega$

Correct answer

A. $\sqrt{2}a\omega$

Step-by-step solution

x = acos \omegat

y = asin \omegat

z = a\omegat

{v}_{x} = - a\omega sin \omegat

{v}_{y} = a\omega cos \omegat

{v}_{2} = a\omega

v = \sqrt{{v}_{x}^{2} + {v}_{y}^{2} + {v}_{z}^{2}}

= \sqrt{{\left(- a\omega sin \omegat\right)}^{2} + {\left(a\omega cos \omegat\right)}^{2} + {\left(a\omega\right)}^{2}}

= a\omega\sqrt{2}

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