solving from v vs t graph

[boogerscout]

Hi all!

I'm really stuck on this problem. I have a v vs t graph showing car A at constant acceleration = 0 m/s2 (horizontal line) with a v=8m/s and car B having a constant acceleration of 3m/s2 (found using slope of the line) with average velocity equal to 6m/s (found by (v2-v1)/2). Here's the question:

 

At t=0, both cars are at x=0. Estimate (a) where and when they meet again and (b) their velocities when they meet.

 

1. I was told that using acceleration I can find x, but I'm thinking I have to do an integral to do this. Is there another way? I was also told this could be solved using a quadratic equation, but I don't understand how. Can anyone give me an idea how to solve this? I don't want the answer (although it may be nice to check my work against), but I would appreciate any input on where to begin.. Thanks in advance.

[Klaynos]

if you use:

 

s=ut+0.5*at^2

 

(u is the initial velocity)

 

Equate for both the systems so:

u₁t+0.5*0*t^2 = u₂t+0.5*3*t^2

 

You can calculate the time, and anything else you need from there...