Plotting the Course

With access to the spacecraft's controls, you connect your computer and begin installing the fuel tank and start capacitor. Your computer informs you that it can plot most of the course to your home planet but needs assistance with determining your velocity and vertical position at a critical moment in time. Your computer provides you with a function that models your acceleration during the first few seconds of flight. You will need to take this information and calculate your velocity and vertical position at time $\backslash ($ t$=2\backslash$mathrm$\{$~s$\}\backslash ).$ Your computer notes that you can use the below initial conditions in supporting your calculations:

Initial time: $0$ s

Initial vertical position: $0$ m

Initial velocity: $\backslash (0\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash )$

Acceleration during this time: $\backslash ($ a$($t$)=52$ t$^\{3\}+53$ t $\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}^\{2\}\backslash )$

What values $($to $2$ decimal places$)$ do you provide your computer?

$\backslash [$

$\backslash$begin$\{$array$\}\{$ll$\}$

v$(2)=$ & $\backslash$mathrm$\{$m$\}/\backslash$mathrm$\{$s$\}\backslash \backslash$

s$(2)=$ & $\backslash$mathrm$\{$m$\}$

$\backslash$end$\{$array$\}$

$\backslash ]$