An Object in Rectilinear Motion Is Moving Along a Horizontal $v ( t ) = \sin ( t )$

Multiple Choice

An object in rectilinear motion is moving along a horizontal line with velocity $v ( t ) = \sin ( t )$ m/s for the time interval $0 \leq t \leq \frac { 3 \pi } { 4 }$ seconds. What is the net displacement from $t = 0$ to $t = \frac { 3 \pi } { 4 }$ ?

A) $\frac { 7 \sqrt { 2 } + 16 } { 12 }$
B) $\frac { \sqrt { 2 } } { 4 }$ m
C) $\frac { \sqrt { 2 } - 8 } { 12 }$ m
D) $\frac { \sqrt { 2 } + 2 } { 2 }$ m
E) $\frac { \sqrt { 2 } + 8 } { 12 }$ m