Calculating Time Required for Overtaking
To calculate the time required for a fast moving vehicle with an acceleration of 1 m/sec² to overtake a slow moving vehicle with a spacing of 25 m, we can follow these steps:

Step 1: Determine the initial velocity of the fast moving vehicle
Given that the fast moving vehicle has an acceleration of 1 m/sec², we can assume that it starts from rest (0 m/s).

Step 2: Calculate the final velocity of the fast moving vehicle
Using the formula v² = u² + 2as, where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the spacing between the two vehicles, we can calculate the final velocity of the fast moving vehicle.

Step 3: Find the time required to reach the final velocity
Using the formula v = u + at, where t is the time taken to reach the final velocity, we can calculate the time required for the fast moving vehicle to reach the final velocity.

Step 4: Calculate the time required for overtaking
Once the fast moving vehicle reaches the final velocity, it will start overtaking the slow moving vehicle. The time required for overtaking can be calculated using the formula t = s/v, where t is the time taken to overtake, s is the spacing between the two vehicles, and v is the velocity of the fast moving vehicle.
By following these steps and plugging in the given values, we can determine the time required for the fast moving vehicle to overtake the slow moving vehicle with a spacing of 25 m.