A train can deccerate at 0.4 m/s. It's traveling at 160km/hr. How far in advance should it apply brakes to come to a full stop.

lol

v = Vi + a t

v = 0 at stop and Vi = 160,000/3600 = 44.4 m/s
so

0 = 44.4 - .4 t
t = 111 seconds

how far in 111 seconds
You can use d = Vi t + (1/2) a t^2
but it is easier just to use the average speed during the stop.
Vav = (44.4 + 0)/3 = 22.2 m/s
d = 22.2 * 111 = 2467 meters
or
2.467 km

This is terrible... this is all wrong! 1) it is (44.4+0)/2 not 3.

I unno how hell you got 111.. but 44.4 + (-.4m/s)^2 is not 111...
and 22.2 x 111 is not 2467... it is 2464.2

Well, let's calculate this with a little bit of humor, shall we?

If the train were to suddenly apply the brakes to come to a full stop, I'm afraid the passengers might have a not-so-pleasant experience. Picture this: a wild, gravity-defying ride where everyone becomes a human cannonball!

But don't worry, we don't want to launch any circus acts. To calculate the distance, we'll need to convert the speed from km/hr to m/s. So, hold on tight!

First, let's convert the speed:
160 km/hr = 160,000 m/3600 s ≈ 44.44 m/s

To calculate the stopping distance, we can use the formula:

Stopping distance = (Initial velocity^2) / (2 * deceleration)

So, plugging in the values, we have:

Stopping distance = (44.44 m/s)^2 / (2 * 0.4 m/s^2)

Calculating this, we get approximately 617.28 meters.

Therefore, the train should apply the brakes about 617.28 meters in advance to come to a full stop.

Just remember, it's always better to apply the brakes early and arrive safely than to try any circus tricks along the way!

To determine how far in advance the train should apply brakes to come to a full stop, we need to calculate the braking distance.

First, let's convert the train's initial velocity from km/hr to m/s.
Given:
Initial velocity (v₀) = 160 km/hr
Convert 160 km/hr to m/s:
v₀ = 160 km/hr * (1000 m/km) * (1 hr/3600 s) = 44.44 m/s (rounded to two decimal places)

Next, we need to calculate the braking distance using the deceleration rate.
Given:
Deceleration (a) = -0.4 m/s² (negative because it's decelerating to come to a stop)
Initial velocity (v₀) = 44.44 m/s
Final velocity (v) = 0 m/s (since the train comes to a full stop)

We can use the following equation of motion to calculate the braking distance (d):

v² = v₀² + 2ad

Rearranging the equation to solve for the braking distance (d):

d = (v² - v₀²) / (2a)

Substituting the values into the equation:

d = (0² - 44.44²) / (2 * -0.4) = 12,345.68 m (rounded to two decimal places)

Therefore, the train should apply the brakes approximately 12,345.68 meters (or about 12.35 kilometers) in advance in order to come to a full stop.