When Will the Two Trains Collide?

[Toranc3]

Homework Statement

The engineer of a passenger train traveling at 25.0 m/s sights a freight train whose caboose is 200 m ahead on the same track. The freight train is traveling at 15.0 m/s in the same direction as the passenger train. The engineer of the passenger train immediately applies the brakes, causing a constant acceleration of 0.100 m/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.

Where will the collision take place?

Homework Equations

y=yo+vo*t+1/2*a*t^(2)

-b+- Sqrt(b^(2)-4ac)/2a

The Attempt at a Solution

yp-passanger train and yf=freight train

Yp=yo+vo*t+1/2*a*t^(2)
yp=25m/s*t - 0.05m/s^(2)*t^(2)

Yf=yo + vo*t +1/2*a*t^(2)
yf=200m +15m/s*t

yp=yf

-0.05m/s^(2)*t^(2) + 10m/s*t -200m

I get t= 177.4596 seconds and t=22.5403 seconds

How do I know which time is correct?

 

[Dick]

Homework Statement

The engineer of a passenger train traveling at 25.0 m/s sights a freight train whose caboose is 200 m ahead on the same track. The freight train is traveling at 15.0 m/s in the same direction as the passenger train. The engineer of the passenger train immediately applies the brakes, causing a constant acceleration of 0.100 m/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.

Where will the collision take place?

Homework Equations

y=yo+vo*t+1/2*a*t^(2)

-b+- Sqrt(b^(2)-4ac)/2a

The Attempt at a Solution

yp-passanger train and yf=freight train

Yp=yo+vo*t+1/2*a*t^(2)
yp=25m/s*t - 0.05m/s^(2)*t^(2)

Yf=yo + vo*t +1/2*a*t^(2)
yf=200m +15m/s*t

yp=yf

-0.05m/s^(2)*t^(2) + 10m/s*t -200m

I get t= 177.4596 seconds and t=22.5403 seconds

How do I know which time is correct?

I haven't checked your numbers. But sure you get two solutions. The later one assumes the trailing train survives the first collision and passes through the leading train and then collides again as the trailing train catches up with it again. Which do you think is the physically plausible one?

 

[Toranc3]

I haven't checked your numbers. But sure you get two solutions. The later one assumes the trailing train survives the first collision and passes through the leading train and then collides again as the trailing train catches up with it again. Which do you think is the physically plausible one?

The 22.5403 seconds one!

 

[Dick]

The 22.5403 seconds one!

I'd agree with that. The first collision is usually the last.

 

[Toranc3]

I'd agree with that. The first collision is usually the last.

Thank you!