$\mathrm{}$$\mathrm{}$Initial Conditions 

In physics, there are special states that we care about. One of these is the initial conditions of a problem. This is just the answer to the question "what are the position and velocity of all of the objects in the problem at the beginning of the problem?" Often this just means, what are the position and velocity at t $=0?$

So$,$ now I$\text{'}$m going to give you the same equation as the one above, but instead I'll fill in the numbers: 

 

 $($t$)=19\mathrm{.}2$ mph $+[22$ mi$/$hr$2]$ t $-[381$ mi$/$hr$3]$ t$2$ 

  

 This and the fact that the billboard is $1000\text{'}$ away, should be enough for you to figure out the initial conditions for this problem. 

  

Write the initial conditions for this problem.

 

 a$)$ What is the initial position of the truck? 

 

$(0)=-1000$

 

 

 $($b$)$ What is the initial velocity of the truck? 

 

 $(0)=19\mathrm{.}2$ mph  

 

 

 

 Part $3$  

 

 $($a$)$ Find the coefficients of the polynomial for the acceleration of the truck. 

 

 a$($t$)=22$mi$/$hr$^2+-762$ mi$/$hr$^3($t$)+0$mi$/$hr$^4($t$^2)+0$mi$/$hr$^5($t$^3)$ 

 

correct

 

 $($b$)$ With the given acceleration, how long would it take to stop in minutes? 

 

 Tf $=?$