A freight train has a mass of 3.2 × 107 kg.
If the locomotive can exert a constant pull
of 7.1 × 105 N, how long would it take to
increase the speed of the train from rest to
74.6 km/h? (Disregard friction.)
change the speed to m/s
F=ma
F=m (change in velocity/time)
F=m * Vfinal/time
solve for time.
To find the time it takes for the train to increase its speed from rest to 74.6 km/h, we can use Newton's second law of motion, which states that the force applied to an object is equal to the mass of the object multiplied by its acceleration.
First, let's convert the final speed of the train from km/h to m/s:
74.6 km/h * (1000 m/km) / (3600 s/h) = 20.7 m/s
Next, we need to know the acceleration of the train. We can use the formula:
acceleration = force / mass
acceleration = (7.1 × 10^5 N) / (3.2 × 10^7 kg) ≈ 0.02219 m/s²
Now, we can use the equation of motion:
final velocity = initial velocity + acceleration * time
Since the train starts from rest, the initial velocity is 0 m/s:
20.7 m/s = 0 m/s + 0.02219 m/s² * time
Simplifying the equation, we can solve for time:
time = (20.7 m/s) / (0.02219 m/s²) ≈ 934.33 seconds
Therefore, it would take approximately 934.33 seconds for the train to increase its speed from rest to 74.6 km/h.