Final answer:
The train moved a distance of 162.5 meters before stopping.
Step-by-step explanation:
To find the distance the train moved before stopping, we can use the equation distance = initial velocity * time + 0.5 * acceleration * time^2. In this case, the initial velocity is 65 m/s (since the train is already moving), the time is 5 s, and the acceleration is the rate at which the train is slowing down, which we don't know. However, since the train comes to a stop, we know the final velocity is 0 m/s. Using the equation final velocity = initial velocity + acceleration * time, we can solve for the acceleration, which turns out to be -13 m/s^2. Substituting the values into the distance equation, we get distance = 65 m/s * 5 s + 0.5 * -13 m/s^2 * (5 s)^2. Solving this equation gives us a distance of 162.5 meters.
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