# Constant Acceleration Problem Involving Two Different Objects

1. Feb 26, 2012

### sb13

1. The problem statement, all variables and given/known data
A car is traveling in the +x direction with a speed v when the driver notices a car that is stopped in front of him a distance d. In order to avoid a collision, he immediately applies the brakes resulting in an acceleration -a1. At the same time, the parked car starts to accelerate in the +x direction with an acceleration of a2. Determine the distance d in terms of v, a1, and a2 if the cars are to just barely avoid a collision.

2. Relevant equations

I'm not sure which constant acceleration formulas to apply but here they all are, just in case:

(1) v=vo+at
(2) x-xo= vot+1/2at^2
(3) v^2= vo^2+2a(x-xo)
(4) x-xo= 1/2(vo+v)t
(5) x-xo=vt-1/2at^2

3. The attempt at a solution

I am not even sure where to begin, but I suppose I would take two of the equations above and make them equal to each other while solving for the distance d (which is x-xo). Since v= vo+at then substitute that into the 5th equation.
x-xo=(vo+at)t-1/2at^2, and change x-xo for d (just to simplify things)
d= (vo+at)t-1/2at^2,
incorporate another equation, equation 4
d= 1/2(vo+(vo+at)t (substitute v for vo+at)

solve for t
d=vot+at^2-1/2at^2
d=t(vo)+t^2(a-1/2a)
d/((vo)(a-1/2a))= t+t^2

I don't know what to do from there.
I don't know if I am heading in the right direction, and I don't know what to do because there are two different accelerations. Also, I don't know what the final answer is supposed to look like.

Last edited: Feb 26, 2012