Problem $2(5$ points$)$

A block of mass $m$ feels a net force of $F(t)=F_0(e^{-at}+t^4)$ where $F_0$ and a are constants.

A$)$ Determine the velocity of the block. $(2$ points$)$

B$)$ Calculate the position of the block. $(2$ points$)$

C$)$ Determine the integration constants by implementing the following initial conditions: $)=(0$ and $)=(0.$ Write out the functions for the velocity and position in terms of the new values of the integration constants. $(1$ point$)$