A freight train has a mass of 1.7 multiplied by 107 kg. If the locomotive can exert a constant pull of 7.4 multiplied by 105 N, how long does it take to increase the speed of the train from rest to 68 km/h?
To find the time it takes to increase the speed of the train, we can use Newton's second law of motion, which states that the force applied is equal to the mass of an object multiplied by its acceleration (F = ma).
First, we need to calculate the acceleration of the train using the given force and mass. The applied force is 7.4 multiplied by 10^5 N, and the mass is 1.7 multiplied by 10^7 kg. Let's calculate the acceleration:
a = F/m
a = (7.4 multiplied by 10^5 N) / (1.7 multiplied by 10^7 kg)
Calculating a = 4.35 m/s^2
Now, we want to find the time it takes to increase the train's speed from rest to 68 km/h. We need to convert the final velocity from km/h to m/s:
Final velocity (vf) = 68 km/h = (68 multiplied by 1000 m) / (3600 s)
vf = 18.9 m/s
To find the time (t), we can use the equation of motion:
vf = u + at
Since the train starts from rest (u = 0), we can simplify the equation to:
t = vf / a
Plugging in the values, we get:
t = 18.9 m/s / 4.35 m/s^2
Calculating t = 4.35 s
Therefore, it takes approximately 4.35 seconds to increase the speed of the train from rest to 68 km/h.