Stopping a Train: Calculating Time from Velocity

[rogetz]

Homework Statement

I have a distance versus velocity graph that gives me the braking distance for a train (for known gradients of track - but gradient is irrevelant for my problem). the graph has distance on the vertical axis and velocity on the horizontal axis. What i want to know is that for a given initial velocity, how long - in time - does it take the train to stop?

Homework Equations

the graph equation i have worked out to be s=2.9u^2 + 29u (where s=distance, u=initial velocity)
(i was given several data points i.e. a train with an intial velocity of x km/h would take y m to stop)

The Attempt at a Solution

i thought i would invert the graph so to make velocity on the vertical and distance on the horizontal. doing this u=-2x10^-5s^2 + 0.09s

using Newtons 2nd (?) law, v=u+at but since v=0 (i.e stopped), then u=-at. what i don't know is a (accelaration - in my case decelleration). but if change in velocity divided by change in time (dv/dt) is accleration and velocity is change in distance divided by change in time (ds/dt) then...

this is where i get lost

please help - it should be easy (i think but i hope not)

 

[diazona]

There's another kinematic equation that might help you:
$$v^2 = u^2 + 2ad$$

P.S. $$v = u + at$$ isn't one of Newton's laws, it's really just math.

 

[nlightner]

I would first commend you on your efforts to use the given data and equations to solve the problem. Your approach is a good start, but I would caution you to be careful with your units and equations. In this case, you are dealing with a deceleration, so the equation v=u+at should be v=u-at, where a is the deceleration.

To calculate the time it takes for the train to stop, you can use the equation v=u-at and solve for t. This will give you the time it takes for the train to decelerate from an initial velocity (u) to a final velocity of 0.

Another approach you could take is to use the equation s=ut+1/2at^2, where s is the distance, u is the initial velocity, a is the deceleration, and t is the time. By substituting the known values for s and u, you can solve for t and get the time it takes for the train to stop.

It's also important to note that the equation s=2.9u^2+29u is not a general equation for all trains, but rather specific to the data points given to you. In real-world scenarios, the deceleration of a train can vary depending on factors such as the weight of the train, the condition of the tracks, and the braking system of the train. So while your approach may work for the given data, it may not be accurate for all trains.

In summary, to calculate the time it takes for a train to stop, you can use the equations v=u-at or s=ut+1/2at^2, where u is the initial velocity and a is the deceleration. However, it's important to consider that these equations may not accurately represent the deceleration of all trains in real-world scenarios.