To calculate the distance covered by the train before coming to rest, we need to determine the time it takes for the train to stop and then use that time to calculate the distance traveled.
First, let's convert the initial velocity of the train from km/hr to m/s: 1 km/hr = 1000 m / (60 * 60) s = 0.2778 m/s So, the initial velocity of the train is 72 km/hr * 0.2778 m/s = 20 m/s.
Next, we can use the following equation of motion to find the time it takes for the train to stop:
v = u + at
Where: v = final velocity (0 m/s, since the train comes to rest) u = initial velocity (20 m/s) a = acceleration (-0.5 m/s^2) t = time
Rearranging the equation to solve for time (t), we have:
t = (v - u) / a
Substituting the given values:
t = (0 m/s - 20 m/s) / (-0.5 m/s^2) t = -20 m/s / -0.5 m/s^2 t = 40 seconds
Therefore, it takes 40 seconds for the train to come to a stop.
Now we can calculate the distance traveled using the formula:
s = ut + (1/2)at^2
Where: s = distance traveled u = initial velocity (20 m/s) t = time (40 seconds) a = acceleration (-0.5 m/s^2)
Plugging in the values:
s = (20 m/s * 40 s) + (0.5 * -0.5 m/s^2 * (40 s)^2) s = 800 m - 400 m s = 400 meters
Hence, the distance covered by the train before coming to rest is 400 meters.