Starting point in linear motion problem

[looptwelve]

Hello all,
I've been working my way through my homework this week, and haven't had much trouble until I hit this question...

Homework Statement

An automobile and a truck start from rest at the same instant, with the automobile initially at some distance behind the truck. The truck has a constant acceleration of 2.07 , and the automobile an acceleration of 3.46 . The automobile overtakes the truck after the truck has moved a distance 42.0 .

The Attempt at a Solution

I answered part A of the question correctly, which was as follows:

How much time does it take the automobile to overtake the truck?
t = 6.37


The parts I can't get are:

How far was the automobile behind the truck initially?
X= ? m

What is the speed of the truck when they are abreast?
v= ? m/s

and

What is the speed of the automobile when they are abreast?
v= ? m/s

Mainly, I'm just not sure how to arrive at the correct equation for the problems. If I could get that I could probably figure them out.

 

[BruceW]

you can either use the equations of motion (suvat), or use calculus. You need to keep in mind that the two vehicles have separate motion.

 

[looptwelve]

Its Physics with Algebra and I'm in the first week of Calculus, so I'd rather steer clear of Calc on this question. What variable do I need to solve for, for "How far was the automobile behind the truck initially"?

 

[BruceW]

I guess the difficult part is imagining the situation. I find making a quick doodle on paper helps. Even if it is not a sketch, just something like 'they are both at the same place at time t=6.37, and at time t=0, they are such a distance apart', and drawing it on paper, like going over the finishing line together, and starting in separate places.

Well, both vehicles had zero initial speed, and so you know the equation to work out their total change in position over some time. (the two vehicles have different accelerations, so these are two different equations). And then you need to apply that to the given situation.

 

[looptwelve]

Hot dog, I got it. I just calculated the displacement for both, and subtracted the auto's from the trucks and finally got it. I don't know why that didn't occur to me yesterday...

Thanks for your help, Bruce.

 

[BruceW]

Sweet, no worries.