Find the Speed of a Particle with the Given Position $r ( t ) = t \mathbf { i } + 5 t ^ { 2 } \mathbf { j } + 3 t ^ { 6 } \mathbf { k }$

Multiple Choice

Find the speed of a particle with the given position function. $r ( t ) = t \mathbf { i } + 5 t ^ { 2 } \mathbf { j } + 3 t ^ { 6 } \mathbf { k }$

A) $| \mathbf { v } ( t ) | = \sqrt { 1 + 100 t ^ { 2 } + 100 t ^ { 10 } }$
B) $| \mathbf { v } ( t ) | = \sqrt { 1 + 100 t + 324 t ^ { 9 } }$
C) $| \mathbf { v } ( t ) | = 1 + 100 t ^ { 2 } + 324 t ^ { 10 }$
D) $| \mathbf { v } ( t ) | = \sqrt { 1 + 100 t ^ { 2 } + 324 t ^ { 10 } }$
E) $| \mathbf { v } ( t ) | = \sqrt { 1 + 100 t + t ^ { 9 } }$