A train that is moving at 25 m/s slows down at a rate of 3 m/s^2 in 4 seconds. How far does it travel while braking?

Sure, here's how to solve this problem:

Step 1: First, we need to find the final speed of the train after braking. We can use the formula for acceleration, which is final speed = initial speed - (acceleration * time). In this case, the initial speed is 25 m/s, the acceleration (actually deceleration, but we'll use a negative number to indicate that) is 3 m/s^2, and the time is 4 seconds. So the final speed is 25 m/s - (3 m/s^2 * 4 s) = 13 m/s.

Step 2: Next, we need to find the distance the train traveled while braking. We can use the formula for distance, which is distance = (initial speed + final speed)/2 * time. So the distance is (25 m/s + 13 m/s)/2 * 4 s = 76 meters.

So the train traveled 76 meters while braking.