How Fast is the Car When It Passes the Train?

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A train moves at a constant speed of 33 m/s while a car, initially 32 m behind, travels at 47 m/s and accelerates at 4 m/s². To determine the car's speed as it passes the train, the displacement equations for both vehicles must be set equal to find the time of intersection. The key is to correctly formulate the equations for displacement in terms of time. Once the time is established, the car's velocity can be calculated at that moment. Understanding these concepts is crucial for solving the problem effectively.
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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!
 
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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...
 

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