Problem with acceleration and distance

[efoster]

Homework Statement

v, a1, a2 are the needed variables

A car is traveling in the +x direction with a speed of v when the driver notices a car that is stopped in front of him at distance d. In order to avoid a collision, he immediately applies the brakes resulting in an acceleration of -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.
The only hint I have is: think about the position and velocity of each car. What is required to just barely avoid a collision.

Homework Equations

f=ma

The Attempt at a Solution

 

[PeterO]

Homework Statement

v, a1, a2 are the needed variables

A car is traveling in the +x direction with a speed of v when the driver notices a car that is stopped in front of him at distance d. In order to avoid a collision, he immediately applies the brakes resulting in an acceleration of -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.
The only hint I have is: think about the position and velocity of each car. What is required to just barely avoid a collision.

Homework Equations

f=ma

The Attempt at a Solution

The hint is telling you provided the cars are traveling at the same speed the two cars could contact each other.

I would start by drawing velocity time graphs for the two cars - well actually the front of the traveling car and the rear of the stopped car