A freight train has a mass of 1.9 107 kg. If the locomotive can exert a constant pull of 7.5 105 N, how long does it take to increase the speed of the train from rest to 90 km/h in minutes?

V = 90 km/h = 25 m/s

a = acceleration rate = F/m = 0.0395 m/s^2

time = V/a = 633 seconds = ___ minutes

To calculate the time it takes to increase the speed of the train, we can use Newton's second law of motion. The formula is:

F = ma

Where F is the force applied, m is the mass of the object, and a is the acceleration.

We can rearrange this equation to solve for acceleration, a:

a = F/m

Given:
Mass of the train, m = 1.9 × 10^7 kg
Force applied by the locomotive, F = 7.5 × 10^5 N

Substituting the given values into the equation, we can calculate the acceleration:

a = (7.5 × 10^5 N) / (1.9 × 10^7 kg)

a ≈ 0.0394 m/s^2

Now, we can use the equation for calculating the time it takes to reach a certain velocity:

v = u + at

Where v is the final velocity, u is the initial velocity (0 m/s in this case, as the train is at rest), a is the acceleration, and t is the time taken.

Given:
Final velocity, v = 90 km/h = (90 × 1000 m/3600 s) m/s = 25 m/s
Initial velocity, u = 0 m/s
Acceleration, a ≈ 0.0394 m/s^2

Substituting the values into the equation, we can solve for time, t:

25 = 0 + (0.0394) t

25 = 0.0394 t

t = 25 / 0.0394

t ≈ 634.5188 s

Converting the time from seconds to minutes:

t ≈ 634.5188 s * (1 min/60 s)

t ≈ 10.575 min

Therefore, it takes approximately 10.575 minutes to increase the speed of the train from rest to 90 km/h.

To find the time it takes for the train to increase its speed, we can use Newton's second law of motion, which states that the force applied to an object is equal to its mass multiplied by its acceleration. In this case, we need to find the acceleration of the train.

First, let's convert the speed from km/h to m/s:
Given speed = 90 km/h
Converting to m/s: 90 km/h * (1000 m/km) / (3600 s/h) ≈ 25 m/s

Since the train is starting from rest, its initial speed (u) is 0 m/s. The final speed (v) is 25 m/s. We can plug these values into the formula for acceleration (a):

v = u + at

Since u = 0, the formula simplifies to:

v = at

Now we can solve for acceleration (a):

a = v / t

where a is the acceleration and t is the time it takes to achieve that acceleration.

Next, let's calculate the acceleration:

a = (25 m/s) / t

We know that force (F) is equal to mass (m) multiplied by acceleration (a):

F = ma

Rearranging this equation, we can solve for acceleration:

a = F / m

Now we can substitute the force and mass values given in the problem:

a = (7.5 * 10^5 N) / (1.9 * 10^7 kg)

Simplifying, we find that the acceleration of the train is approximately 0.0395 m/s².

Now, using the formula v = u + at, we can solve for time (t):

t = (v - u) / a

Substituting the values:

t = (25 m/s - 0) / (0.0395 m/s²)

Calculating, we find that the time it takes for the train to reach a speed of 90 km/h is approximately 634.18 seconds.

To convert this time to minutes, we divide by 60:

t = 634.18 s / 60 ≈ 10.57 minutes

Therefore, it will take approximately 10.57 minutes for the train to increase its speed from rest to 90 km/h.