# Car acceleration calculation problem

1. Sep 20, 2007

### AraProdieur

1. The problem statement, all variables and given/known data
A train is moving parallel and adjacent to a highway with a constant speed of 33 m/s. Initially a car is 32 m behind the train, traveling in the same direction as the train at 47 m/s and accelerating at 4 m/s^2.
What is the speed of the car just as it passes the train? Answer in units of m/s.

2. Relevant equations
So far, I have thought of using delta x= Vot+ 1/2at^2
I also think that I have to account for the displacement between the two trains, which is 14 m.
The thing that I don't understand is how to calculate something as it passes or catches up to another thing.

If there is any advice, thanks!

2. Sep 20, 2007

### bel

Let the point when the measurement starts be s=0, then you have all the initial conditions. Now consider the distance s as a function of time t, so $$s(0)=0$$ for the car and $$s(0)=32$$ for the train. Write two such formulae, one to describe each object. At the point where the car passes the train, the two distances are the same, so you can equate and get a time value $$t_{m}$$, where then you can calculate the speed of the car with the formulae describing uniform acceleration.

3. Sep 20, 2007

### AraProdieur

Yes, but I don't understand how to go about doing that. Like getting the two distances to equal the same? I did think of that as well, but didn't know how to use formulas to do something like that.

4. Sep 21, 2007

### bel

Say, for the train, which is initially (i.e., at time $$t=0$$) 32 metres ahead of the car, and travels with a constant velocity, say $$v_{train}$$. Then we have for the train $$s=32+v_{train}t$$.