Question

A red train traveling at 72 km/hr and a green train traveling at 144 km/hr are headed toward one another along a straight level track. When they are 950 meters apart, each enginneer sees the other's train and applies the brakes. The brakes decelerate each train at the rate of 2.0 m/s^2. Is there a colllision? If so, what is the speed of each train at impact? If not, what is the separtion between the trains when they stop??

Answer 1

the trains do not collide... the separation between them when they stop is 847.97 meters...

Answer 2

That's not the right answer though, and I need help working it out

Answer 3

initial speed of red train=72*5/18=20m/s

initial speed of green train=144*5/18=40m/s

initial separation=950 m

velocity of approach = 20 - (-40)=60 m/s

relative acceleration= -4 m/s^2

v = u + at
0 = 60 - 4t

t= 15s

s= ut + i/2 *at*t

s=60*15 - 1/2 * 4* 225
s = 900 - 450
separation when they stop = 450 m

Answer 4

the first thing we need to do is convert all the parameters into teh same units. We are given speeds in km/hour, and deceleration and distance in m/s\(^2\) and m respectively. So lets convert the speeds to m/s. There are 1000 metres in one kilometre and 3600 seconds in one hour, hence we multiply each speed by 1000, and divide by 3600. This means that the red train is travelling at 20 m/s and teh green train at 40 m/s.

Next we need to know the distance they travel from the point at which they apply the breaks. The deceleration is a = 2 m/s\(^2\) for each train, and we can work out teh distance travelled during breaking using the equation of motion \[V^2=u^2+2as\] and remembering that because it is deceleration, that the sign of a 1ill be negative (i.e. it will be -2 m/s\(^2\)), and that v is teh final velocity (=0) and u is teh initial velocity.
So for the red train, it will travel \[s=\frac{u^2}{2a}=\frac{(20)^2}{2(2)}=100\] So the red train travels 100 meters.

The green train travels \[s=\frac{u^2}{2a}=\frac{(40)^2}{2(2)}=400\]So teh green train travels 400 metres.

Do they collide? The answer is no they don't. The reason why is this. Imaging that we haven't worked the above solution out, but that we know they will not collide. If they dont collide then the we know that the distance the red train travels, plus the distance the green train travels plus the distance of the gap between them must equal 950 metres. If the gap distance is equal to zero (or mathematically less than or equal to zero) the trains will have collided. What this means then is that mathematically if teh sum of the distance the two trains travel is greater than or equal to 950 meters, then they will collide.

Going back to our solutions we see that the sum of the two distances that the trains have travelled is 100+400 = 500 m. Going back to the logic above then, the gap distance between the two trains must then be 950-500 = 450 m.

Hence the trains do not collide, but come to a stop 450 metres apart.

Answer 5

Thanks so much guys!