Calculating Train Deceleration: Kid's Free Fall Time

In summary, the boy falls off the train due to the deceleration, and will land on the floor in 0.8 seconds.
  • #1
ejacques
3
0
Homework Statement
when a high-speed train suddenly begins to decelerate at -5 (m/s^2), a kid sleeping on the upper bunk 3 meter above the floor falls off. where does he land?
Relevant Equations
y=-0.5*g*t^2
I think, since the train is decelerate the kid will fall off at free falling. the time for that is:
y=0.5*9.8*t2 ⇒ t=√(2*y/g)=√(2*3/9.8)=0.8sec.

Now i think i need to find what is the distance the train is doing in this time, but i can't figure this out.
 
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  • #2
How about writing equations for the positions of the kid and the train as a function of time? Take t = 0 when the deceleration starts. Unless the kid falls out an open window, it should land on the floor. The question is how far horizontally from the bed.
 
  • #3
Work in a frame in which the train is stationary. The kid is then initially at rest at [itex](x,y) = (0,3)[/itex]; how does that change when the train starts to decelerate?

Or you can work in an inertial frame in which the train accelerates to the left from rest at [itex]5\, \mathrm{m}\,\mathrm{s}^{-2}.[/itex]
 
  • #4
I still don't get how i can find the train initial velocity, it looks like i need it for the position equ. x(t) of the kid.
why i can work in a frame where the train is stationary?

If i do assume the initial velocity is 0 i do get the answer of 1.5 meters which is the answer given.
again, i don't get why this assumption is valid.
 
  • #5
ejacques said:
I still don't get how i can find the train initial velocity, it looks like i need it for the position equ. x(t) of the kid.
why i can work in a frame where the train is stationary?

If i do assume the initial velocity is 0 i do get the answer of 1.5 meters which is the answer given.
again, i don't get why this assumption is valid.
So, run the equations with an unknown initial velocity ##u## for both train and kid, and see what happens.
 
  • #6
ejacques said:
I still don't get how i can find the train initial velocity, it looks like i need it for the position equ. x(t) of the kid.
why i can work in a frame where the train is stationary?

If i do assume the initial velocity is 0 i do get the answer of 1.5 meters which is the answer given.
again, i don't get why this assumption is valid.
@pasmith gave you two approaches: a non inertial frame in which the train is stationary, or an inertial frame in which the train is initially stationary.

The second may be easier to understand. Imagine you are driving along next to the train at the same velocity. The decelerates but you don't.
You see the boy as falling vertically as the train accelerates backwards. This shows the initial velocity of the train is not relevant.

In the frame of the decelerating train, objects behave as though there is a kind of horizontal gravity in the forward direction. The train is stationary despite the frictional force. The boy will accelerate horizontally at 5m/s2 (as well as vertically).

Of course, you could also work in the ground frame, putting the initial velocity of the train as an unknown. In the ensuing algebra, that unknown will cancel out.
 

FAQ: Calculating Train Deceleration: Kid's Free Fall Time

What is train deceleration?

Train deceleration is the process by which a train reduces its speed over time. It is typically measured in meters per second squared (m/s²) and is an important factor in ensuring the safety and efficiency of train operations.

How do you calculate the deceleration of a train?

To calculate the deceleration of a train, you can use the formula: deceleration (a) = (final velocity (v) - initial velocity (u)) / time (t). If the train comes to a stop, the final velocity is zero. Therefore, the formula simplifies to a = -u / t, where 'u' is the initial velocity and 't' is the time taken to stop.

What is "Kid's Free Fall Time" in relation to train deceleration?

"Kid's Free Fall Time" is a playful term that refers to the time it takes for a child to fall freely under gravity from a certain height. In the context of train deceleration, it can be used as an analogy to help kids understand the concept of deceleration by comparing it to the time it takes for something to fall a certain distance.

How can you relate free fall time to train deceleration?

You can relate free fall time to train deceleration by comparing the acceleration due to gravity (9.8 m/s²) to the deceleration of the train. For example, if a kid's free fall time from a certain height is known, you can use that time to illustrate how quickly a train would need to decelerate to stop within a similar time frame.

Why is understanding train deceleration important?

Understanding train deceleration is crucial for ensuring the safety of passengers and the efficient operation of the train. Properly calculating deceleration helps in designing braking systems, planning safe stopping distances, and preventing accidents. It also aids in optimizing the train's performance and energy consumption.

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