A freight train has a mass of 2.1 × 10^7 kg. If the locomotive can exert a constant pull of 6.2 × 10^5 N, how long would it take to increase the speed of the train from rest to 77.7 km/h? (Disregard friction.)
F=ma
solve for a (a=F/mass)
Vf=at conver km/hr to ms/s, solve for t.
To find the time it takes for the train to accelerate from rest to a certain speed, we need to use Newton's second law of motion.
Newton's second law states that the force acting on an object is equal to the mass of the object multiplied by its acceleration. In this case, the force is provided by the locomotive and the acceleration is what we need to find.
First, we need to convert the speed from km/h to m/s. We know that 1 km/h is equal to 1000 m/3600 s, so:
77.7 km/h = (77.7 * 1000) m/3600 s = 21.5 m/s
Next, we can use the equation Force = mass * acceleration to find the acceleration.
Force = 6.2 × 10^5 N
Mass = 2.1 × 10^7 kg
6.2 × 10^5 N = (2.1 × 10^7 kg) * acceleration
Now, we can solve for acceleration:
acceleration = (6.2 × 10^5 N) / (2.1 × 10^7 kg)
acceleration ≈ 0.0295 m/s^2
Finally, we can use the equation for acceleration to find the time it takes for the train to reach the given speed:
acceleration = change in velocity / time
0.0295 m/s^2 = (21.5 m/s - 0 m/s) / time
Solving for time:
time = (21.5 m/s - 0 m/s) / 0.0295 m/s^2
time ≈ 730.5 s or 12.2 minutes
Therefore, it would take approximately 12.2 minutes for the train to increase its speed from rest to 77.7 km/h.