SOLUTION: The velocity of a train is reduced uniformly from 15m/sec. to 7m/sec. while traveling a distance of 80m. Assuming that the train maintains this constant acceleration, how much fart

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Question 338989: The velocity of a train is reduced uniformly from 15m/sec. to 7m/sec. while traveling a distance of 80m. Assuming that the train maintains this constant acceleration, how much farther will the train travel before coming to a rest?
In this question im very confused about the 15m/sec. to 7m/sec. but overall dont know how to do this problem.
Answer by josmiceli(19441) (Show Source):
You can put this solution on YOUR website!
The speed of the train is becoming
less and less over a certain distance
which they tell you is m
You could make a plot of this as time
on the horizontal axis and distance
traveled on the vertical, but it is easier
to plot distance on the horizontal and
velocity on the vertical.
Let m/sec
Let m/sec
Let the point at which is measured
= m
Let the point at which is measured
= m
-----------------------
In general, the slope of the line is

--------------------------
The general form of the equation for velocity vs distance
would be:

You can see that when , , and
when ,
--------------------------
When the train has stopped, it's velocity is zero, so

This says the train has gone m from where
the 15 m/sec measurement was made. The problem wants to
know how far it went after the 7 m/sec measurement was made
m
The train went more meters before coming to rest
Here is the plot of the line:

Notice that when , and
when ,