A railroad freight car with a mass of 50,000 kg is rolling along a level track at 0.30 m/s. A rope trails behind it. If the maximum force you could apply to stop the cart is 250 N, what is the shortest amount of time (measured in seconds) it would take for you to bring it to rest?
a = Fap/M = -250/50,000 = -0.005 m/s^2.
Vf = Vo + a*t = 0.
t = -Vo/a = 0.30/-0.005 = 60 s.
To calculate the shortest amount of time required to bring the freight car to rest, we need to use the equation of motion:
Force = mass * acceleration
Here we want to calculate the acceleration that can be achieved when applying a maximum force of 250 N. Rearranging the equation:
acceleration = Force / mass
Substituting the given values:
acceleration = 250 N / 50,000 kg
acceleration = 0.005 m/s^2
Now, since the car is initially moving with a velocity of 0.30 m/s, we can calculate the time required to bring it to rest using another equation of motion:
velocity = initial velocity + acceleration * time
Since we want to find the shortest amount of time, we can assume that the final velocity will be zero. Rearranging the equation:
time = (final velocity - initial velocity) / acceleration
Substituting the given values:
time = (0 - 0.30 m/s) / (-0.005 m/s^2)
time = 60 seconds
Therefore, the shortest amount of time it would take to bring the freight car to rest is 60 seconds.