How Fast is the Car When It Passes the Train?

[AraProdieur]

1. Homework Statement
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. Homework 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!

 

[learningphysics]

Get the two equations for displacement/position in terms of time...

to find when they meet, set the two displacements equal... then you can get the velocity of the car at this time...

The main part is getting the two initial equations right...

 

[m2003]

I would suggest using the equation for distance (d) as a function of time (t), which is d= vt+ 1/2at^2. In this case, the car's initial velocity (vo) is 47 m/s and its acceleration (a) is 4 m/s^2. We can also calculate the train's displacement (d) as it travels at a constant speed of 33 m/s for a certain amount of time (t).

To account for the displacement between the two trains, we can subtract the initial distance between them (32 m) from the train's displacement. This will give us the distance the car has to travel to catch up to the train.

Setting the two equations for distance equal to each other (dcar = dtrain - 32 m), we can solve for the time (t) it takes for the car to catch up to the train. Once we have the time, we can plug it into the equation for velocity (v= vo + at) to find the car's final velocity (v) just as it passes the train.

I hope this helps and good luck with your homework!