Physics homework
There's an observer standing next to a railroad track 180m away from the head of a train. When the train's head goes past the observer its velocity is 23m/s. The rear of the train passes the same spot after 4.0 seconds. What's the length of the train? You can assume that acceleration is constant.
How should I start solving this? I tried using different formulas to solve the acceleration and time but I can't get the right answer.
September 27, 2013
9 Comments • Newest first
Nvm, just a misclick.
Solved. Thanks everyone.
Okay, assuming vi=0, we can solve this.
180=1/2*a*t^2 and 23=a*t. We don't really care about how long it took for the train to go from 180m away to the observer, so let's solve directly for a by substituting for t.
t=23/a, so plugging that in, we get 180=1/2*a*(23/a)^2 -> 180=529/(2a) -> a=529/360.
Now, we know that when the head of the train passes the observer, the tail of the train is traveling at the same velocity from a distance D away. We know its velocity and acceleration and time it took to cross that distance D.
Therefore, D=1/2*a*t^2+v*t, so plugging in the values, we get D=4669/45, or ~104 meters.
oh, if the initial velocity is 0 when it is 180m away, then your answer might be 108.8m length of train.
use the formula v^2=v0 + 2a(x-x0)
the v^2 will be 24^2 because that's the speed when it reaches the person. if its initial velocity is 0, then you have 576=2a(x-x0)
the x is 180, and x0 is 0. so you get 576=360a -> a=1.6m/s/s
then you use the x=v0t + 1/2at^2
x=24(4) + 1/2(1.6)(16)
I think the initial velocity is 0m/s and a = constant = ? (since the velocity increases from 0m/s -> 23m/s). And I don't know whether the 4,0 seconds is the time it takes for the rear of the train move 180m+(length of the train) or just the length of the train.
Do we have an initial velocity when it's 180m away? Or should we just assume that a=constant=0?
@MyKarma: sorry, didn't know what CBA meant. i thought it meant chinese basketball association
@simaini:
Read the second part of what I said. I know I'm wrong.
CBA= Can't be asked in case you were wondering.
@mykarma is wrong. there is acceleration, so the speed isn't 23m/s.
i don't remember how to solve the problem, but the first post isn't right
Distance = speed x time. 23 x 4 = 92 meters long
CBA to actually work it out, so free bump?