How Fast Must a Passenger Train Decelerate to Avoid a Crash?

[Woolyabyss]

A passenger train, which is traveling at 80 m/s is 1500 m behind a goods train which is traveling at 30 m/s in the same direction on the same track. At what rate must the passenger train decelerate to avoid a crash?

My attempt at the question:
V=u+at 0=80+at a=-80/t
I tried to find at what time their distances were equal using
s=ut+1/2 (a)(t^2)
80t +1/2 (-80/t) t^2-1500=30t
Simplify and I got 10t=1500
t=150
sub value of t into original equation and you get a=-8/15 m/s^2
The back of my book says its 5/6 m/s^2
Any help would be appreciated

 

[tms]

My attempt at the question:
V=u+at 0=80+at a=-80/t

The passenger train does not have to stop, it just has to slow down to the speed of the freight train before crashing into it.

I tried to find at what time their distances were equal using

That is the right approach.

 

[pongo38]

In your first equation you have used V=0, but to avoid a crash the passenger train only needs to decellerate to 30 m/s

(sorry, tms got there before me with same solution)

 

[Woolyabyss]

Thanks I replaced 0 with 30 in the first equation and carried out the same method as before and got 5/6 m/s^2

 

[Nickie]

To calculate the rate at which the passenger train must decelerate, we need to use the formula for linear acceleration: a=(vf-vi)/t, where vf is the final velocity, vi is the initial velocity, and t is the time interval. In this case, the final velocity of the passenger train must be 30 m/s, as it needs to match the speed of the goods train to avoid a crash. The initial velocity is 80 m/s, and the time interval is the same for both trains, as they are traveling on the same track.

Therefore, we can set up the equation: a=(30-80)/t. We know that the time interval is 150 seconds, as calculated in your attempt. Plugging in the values, we get a=(-50)/150 = -1/3 m/s^2. This means that the passenger train needs to decelerate at a rate of 1/3 m/s^2 in order to avoid a crash with the goods train.

The discrepancy between your answer and the one given in the book could be due to rounding errors or incorrect values used in the calculations. Double-checking your calculations and using more precise values may help in obtaining the correct answer.