A freight train has a mass of 1.7 107 kg. If the locomotive can exert a constant pull of 7.6 105 N, how long does it take to increase the speed of the train from rest to 64 km/h?
To solve this problem, we can use Newton's second law of motion, which states that force is equal to mass times acceleration (F = ma).
First, let's convert the speed from km/h to m/s, since the mass and force are given in SI units.
1 km/h = 1000 m / 3600 s = 0.2778 m/s
Therefore, the speed of the train is 64 km/h * 0.2778 m/s = 17.78 m/s.
Since the train starts from rest, its initial velocity (u) is 0 m/s.
The final velocity (v) is 17.78 m/s.
We can now use the equation of motion: v = u + at, where t represents time and a represents acceleration.
Since the initial velocity is 0, the equation becomes v = at.
Rearranging the equation gives us t = v / a.
Substituting the values, t = 17.78 m/s / (7.6 * 10^5 N / 1.7 * 10^7 kg).
Now, multiply the given force by the given mass: t = 17.78 m/s / (1.7 * 10^7 kg * 7.6 * 10^5 N).
Simplifying the expression, we have t = 17.78 m/s / (1.292 * 10^13 N).
Dividing the speed by the force, we can calculate the time: t = (17.78 m/s) / (1.292 * 10^13 N) ≈ 1.376 * 10^-12 s.
Therefore, it takes approximately 1.376 * 10^-12 seconds to increase the speed of the train from rest to 64 km/h.