Newton's Laws  Summary and Q&A
TL;DR
A train with a mass of 6.84 x 10^6 kg and an initial velocity of 80 km/h is decelerated using brakes with a force of 1.93 x 10^6 N for 25 seconds, resulting in a new velocity and distance traveled.
Questions & Answers
Q: What is the new speed of the train after the brakes are applied for 25 seconds?
To determine the new speed, we calculate the deceleration using the force and mass of the train, and then find the change in velocity. The new speed is calculated to be 55 km/h.
Q: How far does the train travel while braking?
The distance traveled while braking can be calculated by finding the average velocity and multiplying it by the braking time. In this case, the train travels approximately 468.75 meters.
Q: How is acceleration related to force and mass?
According to Newton's second law of motion, the force exerted on an object is equal to the mass of the object multiplied by its acceleration. In this problem, the backward force from the brakes is used to calculate the deceleration of the train.
Q: Why is the acceleration in the opposite direction of the force?
Since the force applied by the brakes is in the opposite direction of the train's velocity, the resulting acceleration will also be in the opposite direction. This negative acceleration causes the train to slow down.
Summary & Key Takeaways

A train with a mass of 6.84 x 10^6 kg is moving at an initial velocity of 80 km/h.

Brakes are applied with a force of 1.93 x 10^6 N for 25 seconds.

The new speed of the train is determined to be 55 km/h, and the distance traveled during braking is 468.75 meters.