Let $\mathbf { a } ( t ) = \cos t \mathbf { i } + \sin t \mathbf { j }$ be the acceleration of an object with velocity $\mathbf { v } ( t )$ . If $\mathbf { v } ( 0 ) = \mathbf { i } + \mathbf { j }$ then the speed $\| \mathbf { v } ( t ) \|$ is

A) $\sqrt { ( \sin t + 2 ) ^ { 2 } + ( \cos t - 1 ) ^ { 2 } }$
B) $\sqrt { ( \sin t - 1 ) ^ { 2 } + ( \cos t + 2 ) ^ { 2 } }$
C) $\sqrt { ( \sin t + 1 ) ^ { 2 } + ( \cos t + 2 ) ^ { 2 } }$
D) $\sqrt { ( \sin t - 1 ) ^ { 2 } + ( \cos t - 2 ) ^ { 2 } }$
E) $\sqrt { ( \sin t + 1 ) ^ { 2 } + ( \cos t - 2 ) ^ { 2 } }$

Question

Let

\mathbf { a } ( t ) = \cos t \mathbf { i } + \sin t \mathbf { j }

be the acceleration of an object with velocity

\mathbf { v } ( t )

. If

\mathbf { v } ( 0 ) = \mathbf { i } + \mathbf { j }

then the speed

\| \mathbf { v } ( t ) \|

is

A) $\sqrt { ( \sin t + 2 ) ^ { 2 } + ( \cos t - 1 ) ^ { 2 } }$
B) $\sqrt { ( \sin t - 1 ) ^ { 2 } + ( \cos t + 2 ) ^ { 2 } }$
C) $\sqrt { ( \sin t + 1 ) ^ { 2 } + ( \cos t + 2 ) ^ { 2 } }$
D) $\sqrt { ( \sin t - 1 ) ^ { 2 } + ( \cos t - 2 ) ^ { 2 } }$
E) $\sqrt { ( \sin t + 1 ) ^ { 2 } + ( \cos t - 2 ) ^ { 2 } }$

Quizplus · Accepted Answer

The Answer of Let $\mathbf { a } ( t ) = \cos t \mathbf { i } + \sin t \mathbf { j }$ be the acceleration of an object with velocity $\mathbf { v } ( t )$ . If $\mathbf { v } ( 0 ) = \mathbf { i } + \mathbf { j }$ then the speed $\| \mathbf { v } ( t ) \|$ is

A) $\sqrt { ( \sin t + 2 ) ^ { 2 } + ( \cos t - 1 ) ^ { 2 } }$
B) $\sqrt { ( \sin t - 1 ) ^ { 2 } + ( \cos t + 2 ) ^ { 2 } }$
C) $\sqrt { ( \sin t + 1 ) ^ { 2 } + ( \cos t + 2 ) ^ { 2 } }$
D) $\sqrt { ( \sin t - 1 ) ^ { 2 } + ( \cos t - 2 ) ^ { 2 } }$
E) $\sqrt { ( \sin t + 1 ) ^ { 2 } + ( \cos t - 2 ) ^ { 2 } }$

Let a(t)=cos⁡ti+sin⁡tj\mathbf { a } ( t ) = \cos t \mathbf { i } + \sin t \mathbf { j }a(t)=costi+sintj

Let $\mathbf { a } ( t ) = \cos t \mathbf { i } + \sin t \mathbf { j }$