# Train chase: collision avoidance

## Homework Statement

The driver of an express train travelling at 38 m/3 [E] sees a freight train 120 m ahead on the same line travelling at a constant velocity of 12 m/2 [E]. He immediately applies his brakes and just avoids a collision. Assume that the freight train maintains its constant velocity. To just avoid the collision the driver of the express train must:

a. reduce his speed to zero
b. reduce his speed to 12 m/s
c. reduce his speed to below 12 m/s
d. reduce his speed but keep well above 12 m/s
e. not possible

## Homework Equations

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Not even sure if we need kinematics equation for this

## The Attempt at a Solution

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I've ruled our options D and E as potential answers.
im not sure if I have to do any calculations or if this is just some sort of theory question

knowns of train:
v1 = 38m/s [E]
dtrain = d

knowns of freigh train
v1 = 12m/s [E]
v2 = 12m/s [E]
a= 0
dfreight train = 120 + d

I tried equating them but there were too many unknown variables in the way

EDIT:
whoops i meant "chase" question

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RUber
Homework Helper
This question is not asking how quickly he has to slow down, but only what are the conditions such that Train 1 does not hit Train 2.
Let me ask a similar question...
If Train 1 is right behind Train 2 and NOT going to hit train 2, what can you say about the relative velocities of the trains?

their relative velocties would be the same i believe

so the question I have now is that to just avoid collision, if the train reduces its speed to the same as the freight train, they would never collide correct? But then again if the train reduces its speed to zero then they would never collide either. also if the train reduces its speed to below that of the freight train then they would never collide either

RUber
Homework Helper
Right on all counts. So the most correct answer would be the least significant change necessary to just avoid the collision.

So that would mean reducing the train's speed to 12 m/s i assume

haruspex
Homework Helper
Gold Member
if the train reduces its speed to the same as the freight train, they would never collide correct?
That does not follow.
The question statement bothers me. None of the options is a necessary and sufficient condition to avoid a collision. One of them is the least necessary action of those listed, and you have correctly identified it. But whether a collision is thereby avoided depends on how quickly the train's speed reduces.
And what really bothers me about the question is the word "just". That doesn't sit well with the list of options at all.

Edit: Please double check that you have posted the entire question, word for word.

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