Will the Passenger Train Stop Before Hitting the Freight Train?

[mopar969]

The engineer of a passenger train traveling at 25m/s sights a freight train whose caboose is 200m ahead on the same track. The freight train is traveling at 15m/s in the same direction as the passenger train. The engineer of the passenger train immediately applies the brakes, causing a constant acceleration of -0.1m/s^2, while the freight train continues with constant speed. Take x=0 at the location of the front of the passenger train when the engineer applies the brakes.
a): Will the cows nearby witness a collision?
b):If so, where will it take place?
c):On a single graph, sketch the positions of the front of the passenger train and the back of the freight train.

Please help me start this problem. What equations do I need to find out if the trains collide?

 

[kjohnson]

You should be able to solve it with the principle of relative motion.. what is the velocity of the passenger train relative to the freight train? Then use the basic equations of motion to find out how long it takes to stop.

 

[mopar969]

Okay, I'm understanding you but I need an equation to find t (how long till the train stops)? Any ideas?

 

[mopar969]

Any Ideas on What equations I need?

 

[kjohnson]

Thats just your basic motion equations:

vf=vo+at

 

[mopar969]

What value do I use for t though or am I solving for t then what is my vf value? Please help.

 

[mopar969]

I got a friend to help me out however I wanted to check my answer. I calculated that the trains will collide at 1700m from the front of the passenger train. Is my answer right?

 

[kjohnson]

I would check your calculations..first calculate the time it takes for the two trains to collide. You can do this using relative motion, by finding the position x(t) where the initial velocity is the relative velocity and setting it to zero, or set up the two equations of motion x1(t) and x2(t) using actual given values of velocity/position and set them equal to each other. Either one will result in the same second order equation where you can solve for time. Now that you know the time it takes the two trains to collide, figure out how long it takes the passenger train to stop using the equation vf=vo+at where vo must equal the actual velocity (not relative).