A heavy freight train has a mass of 14000 metric tons. If the locomotive can pull with a force of 645000 N, how long does it take to increase it's speed from 0 to 69.8 km/h?

To determine the time it takes for the heavy freight train to increase its speed from 0 to 69.8 km/h, we can use Newton's second law of motion:

Force = mass × acceleration

First, we need to convert the mass of the train from metric tons to kilograms. There are 1000 kilograms in one metric ton, so the mass of the train is:

Mass = 14000 metric tons × 1000 kg/metric ton = 14,000,000 kg

Next, we need to convert the speed of the train from km/h to m/s. There are 1000 meters in one kilometer and 3600 seconds in one hour, so the speed of the train is:

Speed = 69.8 km/h × 1000 m/km × (1 h / 3600 s) = 19.4 m/s

Now, we can find the acceleration of the train using the formula:

acceleration = change in velocity / time

Since the train starts from rest (0 velocity), the change in velocity is equal to the final velocity. Therefore, the acceleration is:

acceleration = (19.4 m/s - 0 m/s) / time

Now, we can rearrange the equation to solve for time:

time = (19.4 m/s) / acceleration

To find the acceleration, we can use Newton's second law of motion:

Force = mass × acceleration

Rearranging the equation:

acceleration = Force / mass

Substituting the values we have:

acceleration = 645,000 N / 14,000,000 kg

Now, we can substitute the value of acceleration back into the equation for time:

time = (19.4 m/s) / (645,000 N / 14,000,000 kg)

Calculating the result:

time = (19.4 m/s) × (14,000,000 kg / 645,000 N)

time ≈ 420.78 seconds

Therefore, it takes approximately 420.78 seconds for the heavy freight train to increase its speed from 0 to 69.8 km/h.