The position co-ordinates of a particle moving in a 3-D coordinate system is given by x = a cos ω t y = a sin ω t and z = a ω t The speed of the particle is :

Question

The position co-ordinates of a particle moving in a 3-D coordinate system is given by x = a cos ω t y = a sin ω t and z = a ω t The speed of the particle is : (A) a ω (B) √3 a ω (C) √2 a ω (D) 2 a ω

Tardigrade Admin · Accepted Answer

vx = - a ω sinω t ⇒ vy = a ω cosω t vz = a ω ⇒ v = √v2x + v2y +v2z v = √2 a ω

Q. The position co-ordinates of a particle moving in a 3-D coordinate system is given by
$x = a cos ω t$
$y = a sin ω t$
and $z = aω t$
The speed of the particle is :

$aω$

$3 aω$

$2 aω$

$2 aω$

$v_{x} = - aω sin ω t \Rightarrow v_{y} = aω cos ω t$
$v_{z} = aω \Rightarrow v = v_{x}^{2} + v_{y}^{2} + v_{z}^{2}$
$v = 2 aω$

Q. The position co-ordinates of a particle moving in a 3-D coordinate system is given by x=acosωt y=asinωt and z=aωt The speed of the particle is :

aω

3​aω

2​aω

2aω

vx​=−aωsinωt⇒vy​=aωcosωt vz​=aω⇒v=vx2​+vy2​+vz2​​ v=2​aω

Q. The position co-ordinates of a particle moving in a 3-D coordinate system is given by
$x = a cos ω t$
$y = a sin ω t$
and $z = aω t$
The speed of the particle is :

$aω$

$3 aω$

$2 aω$

$2 aω$

$v_{x} = - aω sin ω t \Rightarrow v_{y} = aω cos ω t$
$v_{z} = aω \Rightarrow v = v_{x}^{2} + v_{y}^{2} + v_{z}^{2}$
$v = 2 aω$