A train moves along a straight track towards a road crossing with a speed of 85.0 km/hr. At the moment the front car of the train arrives at the crossing the conductor applies the brakes which decelerates the train at a constant rate. If the train is 6.00 × 102 m long, and the end of the last
car passes the crossing with a speed of 14.0 km/hr, how long (in minutes) was the train blocking the road at the crossing? You may ignore the width of the crossing.
avg speed=(14+85)/2 km/hr=13.6 m/s
time= distance/velocity=600/13.6 seconds
length = stopping distance = 600 meters
I assume you mean 10^2 = 100
Vi = 85 /3.6 = 23.6 meters/second
average speed during stop = 23.6/2 = 11.8 m/s
time to go 600 meters = 600/11.8 = 50.8 seconds
just under a minute
whoops, sorry, thought it stopped, use Pursley average speed
To find out how long the train was blocking the road at the crossing, we need to determine the time it took for the entire train to cross the road.
First, let's convert the speeds from km/hr to m/s for consistency:
Speed of the train (initial): 85.0 km/hr = (85.0 × 1000) m/3600 s = 23.61 m/s
Speed of the last car (final): 14.0 km/hr = (14.0 × 1000) m/3600 s = 3.89 m/s
Now, let's calculate the acceleration of the train using the formula:
v^2 = u^2 + 2as
where:
v = final velocity = 3.89 m/s (speed of the last car)
u = initial velocity = 23.61 m/s (speed of the train)
a = acceleration (negative, as it is deceleration)
s = distance = length of the train = 6.00 × 10^2 m
Rearranging the formula to solve for acceleration (a):
a = (v^2 - u^2) / (2s)
a = (3.89^2 - 23.61^2) / (2 × 6.00 × 10^2)
a = -0.065 m/s^2
Now, we can use the formula of motion to find the time it took for the entire train to cross the road:
v = u + at
where:
v = final velocity = 0 m/s (as the train comes to a stop)
u = initial velocity = 23.61 m/s
a = acceleration = -0.065 m/s^2 (negative, as it is deceleration)
t = time
Rearranging the formula, we get:
t = (v - u) / a
t = (0 - 23.61) / (-0.065)
t = 364.0 seconds
Finally, let's convert the time from seconds to minutes:
t = 364.0 s × (1 min / 60 s) = 6.07 minutes
Therefore, the train was blocking the road at the crossing for approximately 6.07 minutes.