A heavy freight train has a mass of 11800 metric tons. If the locomotive can pull with a force of 691000 N, how long does it take to increase it's speed from 0 to 70.3 km/h?
To find the time it takes for the heavy freight train to increase its speed from 0 to 70.3 km/h, we need to use Newton's second law of motion:
F = m * a
Where:
F is the force,
m is the mass, and
a is the acceleration.
In this case, we have the force (F) of 691,000 N and the mass (m) of the train, which is 11,800 metric tons. However, we need to convert the mass from metric tons to kilograms as the SI units for force and mass should be consistent.
1 metric ton = 1000 kilograms
So, the mass of the train in kilograms is:
Mass = 11,800 metric tons * 1000 kg/metric ton = 11,800,000 kg
Now, we can rearrange the formula to solve for acceleration:
a = F / m
Plugging in the values:
a = 691,000 N / 11,800,000 kg
Calculating this gives us an acceleration (a) of approximately 0.0586 m/s^2.
Next, we need to determine the time it takes for the train to increase its speed from 0 to 70.3 km/h. We can use the formula:
v = u + at
Where:
v is the final velocity,
u is the initial velocity (0 in this case),
a is the acceleration, and
t is the time.
We need to convert the final velocity of 70.3 km/h to meters per second:
1 km/h = 1000 m / 3600 s ≈ 0.278 m/s
So, the final velocity (v) is:
v = 70.3 km/h * 0.278 m/s per km/h ≈ 19.5154 m/s
Now we can solve for time (t):
t = (v - u) / a
Plugging in the values:
t = (19.5154 m/s - 0 m/s) / 0.0586 m/s^2
Calculating this gives us a time (t) of approximately 333 seconds.
Therefore, it takes approximately 333 seconds for the train to increase its speed from 0 to 70.3 km/h.