(adsbygoogle = window.adsbygoogle || []).push({}); 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.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Constant Acceleration Problem Involving Two Different Objects

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**