Vector dynamics question starting from accelaration

[vladilinsky]

Homework Statement

I took this right out of the text, it is not home work just me trying to get better.

The acceleration of a particle is defined by the relation a = -8 m/s^2
Knowing that x = 20 m when t= 4 m, and that x = 4 m when v = 16 m/s
(a) determine the time when velocity is zero and (b) the velocity and total distance traveled when t = 11 s

Homework Equations

The Attempt at a Solution

My attempt is I know velocity must be the integration of acceleration and displacement the integration of velocity. So I attempted to integrate -8dt 2 times. but when I do that I get x=-4t^2 which does not fit my given when t=4, x=20
Any help would be greatly appreciated, even just pointing me in the right direction

 

[fss]

Looks like you need to take initial conditions into account. Remember that when you integrate you have a constant of integration as well, which you can determine if you have initial conditions (which you have).

 

[vladilinsky]

How do I know which of the conditions to use for the initial conditions?