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The velocity, in feet per second, of a particle moving along the $x$-axis is given by the function $v(t)=4e^{-t}+\frac{1}{2}t^{2}$.

What is the average velocity of the particle from time $t = 0$ to time $t = 4$?

A

$1.018\ \cfrac { \text{ft} }{ \text{sec} } $

B

$3.648\ \cfrac{ \text{ft} }{ \text{sec} } $

C

$8.073\ \cfrac { \text{ft} }{ \text{sec} } $

D

$14.593\ \cfrac { \text{ft} }{ \text{sec} } $

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