$\text { Find the velocity vector in terms of } u _ { r } \text { and } u _ { \theta } \text {. }$
-$\mathrm { r } = \mathrm { e } ^ { \mathrm { a } \theta } \text { and } \frac { \mathrm { d } \theta } { \mathrm { dt } } = 3$
A) $\mathbf { v } = 3 a \mathrm { e } ^ { \mathrm { a } \theta _ { \mathbf { u } _ { \mathrm { r } } } + 3 \mathrm { e } ^ { \mathrm { a } \theta _ { \mathbf { u } } } \mathbf { u } _ { \theta } }$
B) $\mathbf { v } = 3 a \mathrm { e } ^ { \mathrm { a } \theta _ { \mathbf { u } _ { \mathrm { r } } } + 3 a \mathrm { e } ^ { \mathrm { a } \theta _ { \mathbf { u } } } \mathbf { u } _ { \theta } }$
C) $\mathbf { v } = 3 e ^ { a \theta _ { \mathbf { u } _ { \mathrm { r } } } + 3 a \mathrm { e } ^ { \mathrm { a } \theta _ { \mathbf { u } } } }$

Question

Quizplus · Accepted Answer

The velocity vector is given by:$$\mathbf { v } = \frac { d \mathbf { r } } { d t } = \frac { d } { d t } \left( \mathrm { e } ^ { \mathrm { a } 	heta } ight) \mathbf { u } _ { \mathrm { r } } + \mathrm { e } ^ { \mathrm { a } 	heta } \frac { d 	heta } { d t } \mathbf { u } _ { 	heta }$$$$= a \mathrm { e } ^ { \mathrm { a } 	heta } \frac { d 	heta } { d t } \mathbf { u } _ { \mathrm { r } } + \mathrm { e } ^ { \mathrm { a } 	heta } \frac { d 	heta } { d t } \mathbf { u } _ { 	heta }$$$$= 3 a \mathrm { e } ^ { \mathrm { a } 	heta } \mathbf { u } _ { \mathrm { r } } + 3 \mathrm { e } ^ { \mathrm { a } 	heta } \mathbf { u } _ { 	heta }$$

Find the velocity vector in terms of ur and uθ. \text { Find the velocity vector in terms of } u _ { r } \text { and } u _ { \theta } \text {. } Find the velocity vector in terms of ur​ and uθ​.

$\text { Find the velocity vector in terms of } u _ { r } \text { and } u _ { \theta } \text {. }$