A freight train has a mass of 1.6 × 10
7
kg.
If the locomotive can exert a constant pull
of 8.0 × 10
5
N, how long would it take to
increase the speed of the train from rest to
80.3 km/h? Disregard friction
To determine how long it would take to increase the speed of the train, we can use Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.
We can start by calculating the acceleration of the train using the given force and mass. The formula for acceleration is:
a = F / m,
where a is the acceleration, F is the net force, and m is the mass.
Plugging in the values, we get:
a = (8.0 × 10^5 N) / (1.6 × 10^7 kg)
= 0.05 m/s^2
Now, we need to find the time it takes for the train to increase its speed from rest (initially 0 m/s) to 80.3 km/h. We need to convert the final speed to m/s to be consistent with the units of acceleration.
1 km/h = 1000 m/3600 s = 0.2778 m/s
Thus, 80.3 km/h = 80.3 × 0.2778 m/s = 22.32 m/s.
We can use the formula for accelerated motion to find the time:
v = u + at,
where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time.
Since the train starts from rest (u = 0 m/s), we have:
t = (v - u) / a
= (22.32 m/s - 0 m/s) / 0.05 m/s^2
= 446.4 s.
Therefore, it would take approximately 446.4 seconds (or about 7.4 minutes) to increase the speed of the train from rest to 80.3 km/h, disregarding friction.