A Runaway Train Car Physics Calculation

Calculating the Time Required to Stop a Runaway Train Car

A runaway train car that has a mass of 15,000 kg travels at a speed of 5.4 m/s down a track. To stop this train car, a force of 1500 N is applied. How long will it take for the train car to come to a complete stop?

Final answer:

To stop a runaway train car of 15,000 kg traveling at 5.4 m/s with a 1500 N force, it takes 54 seconds, calculated using Newton's second law of motion.

Explanation:

The question asks to compute the time required for a force of 1500 N to bring a runaway train car with a mass of 15,000 kg and an initial speed of 5.4 m/s to rest. To find this time, we use the formula derived from Newton's second law of motion and the definition of acceleration (change in velocity over time). The required equation is time (t) = change in velocity (Δv) / acceleration (a), where acceleration is produced by the force applied (F) on the mass (m) of the train car, so a = F/m. The train comes to rest, so the final velocity is 0 m/s, and the change in velocity (Δv) is the initial velocity, which is 5.4 m/s in the opposite direction of the force.

First, we calculate acceleration:
a = F/m = 1500 N / 15,000 kg = 0.1 m/s².

Next, we find time:
t = Δv / a = 5.4 m/s / 0.1 m/s² = 54 seconds.

Therefore, it takes 54 seconds for the force to bring the train car to rest.