physics

A red train traveling at 72 km/h and a green train traveling at 144 km/h are headed toward one another along a straight, level track. When they are 950m apart, each engineer sees the other’s train and applies the brakes. The brakes decelerate each train at the rate of 1 m/s^2. Is there a collision? If so what is the speed of each train at impact? If not what is the separation between the trains when they stop?

I will be happy to critique this for you. Hint: The distance the slower train travels is 1/2 the faster train. So see if the slow train can stop in 950(2/3) m.

Vf^2= vo^2 - 2ad
change Vo to m/s If you get a solution here with vf=0 for d less than 2/3 950, then they do not collide.

I got d as 800m for the faster train. so they do collide. To find the speed of each train what would I have to do?


We have two objects and velocities: red 72km/h, green 144km/h.
You should convert each velocity to m/s for compatibility. 1km/hr = 1000m/3600s = 10m/36s =5m/18s.
(BTW, you should learn some basic conversions. It's definitely worth memorizing this one.)
The velocity of the red train is
72*5/18 m/s= 20m/s and the green train's velocity is 40m/s
Let's look at the distance the red one travels in decelerating. The formula is given by
(1)v_f^2= v_o^2 + 2ad so d=(v_f^2 - v_o^2)/2a
For the red train v_f=0m/s, v_o=20m/s
and a=-1m/s^2 then d=(0-400)/-1 m = 400m
For the green train v_f=0m/s, v_o=40m/s and a=-1m/s^2 then
d=(0-1600)/-1 m = 1600m
They do collide.
I should point out this is not a linear equation, so we can't simply double the distance for the second one.
The distance needed for each is proportional to the square of the velocity.
Let d1 be the distance the red one travels and d2 the distance for the green one. The distances are related by
d1+d2=950m and d1:400=d2:1600 so d2=4d1 and
5d1=950 or d1=190 and d2=760
Now using (1) above for the red train, we have
v_f=sqrt(v_o^2 + 2ad) where v_o=20m/s and a=-1m/s^2 so v_f= sqrt(20)m/s
For the green train the calculations are similar.
v_f=sqrt(v_o^2 + 2ad) where v_o=40m/s and a=-1m/s^2 so v_f= sqrt(1220)m/s
In this problem it appears the green train barely starts to decelerate when they collide.

Be sure to check my calculations and that I used the formulas correctly.
I only worked this because it's been asked about 5 times now and you'll probably need this for either a quiz or test soon.


I see I got the velocity v_f of the green train wrong. I used the same distance for it as the red one. The formula is
v_f=sqrt(v_o^2 + 2ad) where v_o=40m/s and a=-1m/s^2 and d=760m so
v_f=sqrt(1600-2*(-1)*760)=sqrt(80) for the green train.
I 'think' I got the red one right, but check it just the same.

  1. 👍
  2. 👎
  3. 👁
  1. GOOD!!!thanks you

    1. 👍
    2. 👎
  2. (1)v_f^2= v_o^2 + 2ad so d=(v_f^2 - v_o^2)/2a
    For the red train v_f=0m/s, v_o=20m/s
    and a=-1m/s^2 then d=(0-400)/-1 m = 400m

    this statement is wrong-- you failed to multiply the acceleration by 2 as it states in the equation. So (vx^2-vx0^2)/2(ax)= x
    so therefore--(0-400)/(2*-1)= 200m=x

    1. 👍
    2. 👎
  3. there also is a problem with the vaster train's distance. Make sure to divide by two. Dividing in this instance makes the d of the faster train 800 instead of 1600. These different numbers don't change the fact that they collided, though, considering d1+d2=total, which is 200+800=1000, which is greater than 950.

    1. 👍
    2. 👎
  4. So I'm still confused on what's happening here?

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. physics

    An automobile traveling 95 overtakes a 1.10--long train traveling in the same direction on a track parallel to the road. Q1: If the train's speed is 75 , how long does it take the car to pass it Q2:How far will the car have

  2. physics

    A red train traveling at 72 km/h and a green train traveling at 144 km/h are headed toward each other along a straight, level track. When they are 720 m apart, each engineer sees the other's train and applies the brakes. The

  3. Physics

    the engineer of a passenger train traveling at 100 ft/sec sights a freight train whose caboose is 600 ft ahead of the same track. The freight train is traveling in the same direction as the passenger train with a velocity of 30

  4. physics

    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

  1. physics

    2. A freight train traveling with a velocity of 18.0 m/s to the south begins braking as it approaches the train yard. The train’s acceleration while braking is -0.33m/s2. What is the train’s speed after 23 seconds?

  2. Help

    I have tried to solve this problem several time sto get the answer and I am lost. Train A and B are traveling in the same direction on parallel tracks. Train A is traveling at 80 miles per hr abd train B is traveling at 90 miles

  3. algebra

    Trains A and B are traveling in the same direction on parallel tracks. Train A is traveling at 100 mph and train B is traveling at 110 mph. Train A passes a station at 3:10 pm. If train B passes the same station at 3:40pm, at what

  4. algebra

    Train A and B are traveling in the same direction on parallel tracks. Train A is traveling at 100 mph and B is traveling at 120 mph. Train A passes a station at 9:10 pm. If train B passes the same station at 9:25pm what time will

  1. math-word problem-please help

    Train A and B are traveling in the same direction on parallel tracks. Train A is traveling at 100 miles per hour and train B is traveling at 120 miles per hour. Train A passes a station at 5:20am. If train B passes the same

  2. algebra

    trains A and B are traveling in the same direction on paraleel tracks. Train A is traveling at 80 miles per hour and train B is traveling at 88 miles per hour. Train a passes a station at 5:10 P.M. If train B passes the same

  3. Physics

    the engineer of a passenger train traveling at 25.0 m/s sights a freight train whose caboose is 200m 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

  4. Math

    5) A freight train leaves a station traveling at 32 km/h. Two hours later, a passenger train leaves the same station traveling in the same direction at 52 km/h. How long does it takes the passenger train to catch up to the freight

You can view more similar questions or ask a new question.