A freight train has a mass of 5 x 107 kg. If the locomotive can exert a constant pull of 12 x 105 N, how long would it take to increase the speed of the train from rest to 85 km/h

m=5*107 kg

F=12*105 N
a=F/m m/s²
Time, t, to reach 85 km/h = V m/s (conversion required)
t=V/a seconds

To calculate the time it takes to increase the speed of the train from rest to 85 km/h, we can use Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.

First, we need to find the net force acting on the train. The net force is equal to the product of mass and acceleration. In this case, the acceleration is the change in velocity divided by the time, and since the train starts from rest, the initial velocity is zero. Therefore, the acceleration can be determined as follows:

acceleration = change in velocity / time

Since the final velocity is 85 km/h and the initial velocity is 0, the change in velocity is 85 km/h. However, it's important to convert this velocity into m/s for consistent units.

1 km/h = 1000 m / (60 * 60) s = 1/3.6 m/s

So, 85 km/h is equal to:

85 km/h * (1/3.6) m/s = 23.61 m/s

Now we can calculate the acceleration:

acceleration = 23.61 m/s / time

Next, we need to find the force required to accelerate the train. The force can be calculated using Newton's second law of motion by rearranging the formula:

force = mass * acceleration

Given a mass of 5 x 10^7 kg and acceleration calculated above, we have:

force = (5 x 10^7 kg) * (23.61 m/s) / time

Now we can equate the force provided by the locomotive to the force required for acceleration:

12 x 10^5 N = (5 x 10^7 kg) * (23.61 m/s) / time

To find the time it takes to increase the speed of the train, we can rearrange the equation as follows:

time = (5 x 10^7 kg) * (23.61 m/s) / (12 x 10^5 N)

Calculating the time:

time = (5 x 10^7 kg * 23.61 m/s) / (12 x 10^5 N)
= (1.1805 x 10^9 kg m/s) / (12 x 10^5 N)
= 0.98375 x 10^4 s
= 9837.5 s

Therefore, it would take approximately 9837.5 seconds (or 2 hours and 44 minutes) to increase the speed of the train from rest to 85 km/h.