Let $\mathbf { a } ( t ) = - 9.5 \mathbf { k }$ be the acceleration of an object with velocity $\mathbf { v } ( t )$ . If $\mathbf { v } ( 0 ) = 2 \mathbf { i } + 3 \mathbf { j }$ then the speed $\| \mathbf { v } ( t ) \|$ is

A) $\sqrt { 90.25 t ^ { 2 } + 15 }$
B) $\sqrt { 90.25 t ^ { 2 } - 25 }$
C) $\sqrt { 90.25 t ^ { 2 } + 13 }$
D) $\sqrt { 90.25 t ^ { 2 } + 5 }$
E) $\sqrt { 90.25 t ^ { 2 } - 13 }$

Question

Let

\mathbf { a } ( t ) = - 9.5 \mathbf { k }

be the acceleration of an object with velocity

\mathbf { v } ( t )

. If

\mathbf { v } ( 0 ) = 2 \mathbf { i } + 3 \mathbf { j }

then the speed

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

is

A) $\sqrt { 90.25 t ^ { 2 } + 15 }$
B) $\sqrt { 90.25 t ^ { 2 } - 25 }$
C) $\sqrt { 90.25 t ^ { 2 } + 13 }$
D) $\sqrt { 90.25 t ^ { 2 } + 5 }$
E) $\sqrt { 90.25 t ^ { 2 } - 13 }$

Quizplus · Accepted Answer

The velocity in the k direction is $-9.5t$, so the speed is $\sqrt{(2)^2 + (3)^2 + (-9.5t)^2} = \sqrt{4 + 9 + 90.25t^2} = \sqrt{90.25t^2 + 13}$.

Let a(t)=−9.5k\mathbf { a } ( t ) = - 9.5 \mathbf { k }a(t)=−9.5k

Let $\mathbf { a } ( t ) = - 9.5 \mathbf { k }$