B

Step 1: Determine the relative speed of train A with respect to train B.
Since both trains are moving in the same direction, we can calculate the relative speed as follows:
$$ v_{rel} = v_A - v_B = 25 ext{ m/s} - 15 ext{ m/s} = 10 ext{ m/s} $$
Step 2: Calculate the time taken for train A to stop after brakes are applied. Since train A has a deceleration of 1.0 m/s², we can use the formula for final velocity under constant acceleration:
$$ v_f = v_i + a t $$
Setting final velocity ($ v_f $) to 0 (come to rest), we have:
$$ 0 = 25 ext{ m/s} - 1 ext{ m/s}^2 imes t $$
Rearranging gives us:
$$ t = \frac{25 ext{ m/s}}{1 ext{ m/s}^2} = 25 ext{ s} $$
Step 3: Calculate the distance travelled by train A before it comes to a stop. We will use the formula:
$$ d_A = v_i t + \frac{1}{2} a t^2 $$
Plugging in the values:
$$ d_A = 25 ext{ m/s} \times 25 ext{ s} + \frac{1}{2} (-1 ext{ m/s}^2) (25 ext{ s})^2 $$
$$ d_A = 625 ext{ m} - \frac{1}{2} \times 1 imes 625 $$
$$ d_A = 625 ext{ m} - 312.5 ext{ m} = 312.5 ext{ m} $$
Step 4: Calculate the distance travelled by train B during the same time.
Train B's speed is 15 m/s, so the distance travelled by train B in 25 seconds is:
$$ d_B = v_B \times t = 15 ext{ m/s} \times 25 ext{ s} = 375 ext{ m} $$
Step 5: To avoid collision, the distance between the two trains must be at least the distance travelled by train B minus the distance travelled by train A:
$$ D_{min} = d_B - d_A = 375 ext{ m} - 312.5 ext{ m} = 62.5 ext{ m} $$
Therefore, to avoid an accident, the minimum distance between the trains should be 62.5 m.