Given:
- Object starts from rest
- Distance travelled in the first 5 seconds = 50 m
- Distance travelled in the next 10 seconds = 400 m

To Find:
- Velocity of the object after 12 seconds from the start

Explanation:

1. Calculating Average Velocity:
Average velocity can be calculated by dividing the total distance travelled by the total time taken. We can calculate the average velocity for the first 5 seconds and the next 10 seconds separately.

- Average velocity for the first 5 seconds:
The object travels 50 m in the first 5 seconds, so the average velocity for the first 5 seconds is:
Average velocity = Distance travelled / Time taken
Average velocity = 50 m / 5 s
Average velocity = 10 m/s

- Average velocity for the next 10 seconds:
The object travels 400 m in the next 10 seconds, so the average velocity for the next 10 seconds is:
Average velocity = Distance travelled / Time taken
Average velocity = 400 m / 10 s
Average velocity = 40 m/s

2. Calculating Final Velocity:
To calculate the final velocity after 12 seconds, we need to consider the acceleration of the object. Since the object starts from rest, the acceleration will be constant.

- For the first 5 seconds:
Since the object starts from rest, the initial velocity is 0 m/s. We can use the equation of motion to calculate the final velocity after 5 seconds:
Final velocity = Initial velocity + (Acceleration * Time)
Final velocity = 0 m/s + (Acceleration * 5 s)
Final velocity = 5A

- For the next 10 seconds:
The object continues to move with a constant acceleration, so the final velocity after 10 seconds can be calculated using the equation of motion:
Final velocity = Initial velocity + (Acceleration * Time)
Final velocity = 10 m/s + (Acceleration * 10 s)
Final velocity = 10 + 10A

3. Using the Concept of Average Velocity:
We can also use the concept of average velocity to calculate the final velocity after 12 seconds. Since the average velocity is constant for each interval, we can take the average of the two average velocities calculated earlier.

- Average velocity for the first 5 seconds = 10 m/s
- Average velocity for the next 10 seconds = 40 m/s

Taking the average of these two velocities, we get:
Average velocity = (10 m/s + 40 m/s) / 2
Average velocity = 50 m/s / 2
Average velocity = 25 m/s

4. Conclusion:
- The final velocity after 12 seconds from the start can be calculated using either the equations of motion or the concept of average velocity.
- Using the equations of motion, the final velocity after 12 seconds is given by the equation: Final velocity = 5A + 10 + 10A, where A is the constant acceleration.
- Using the concept of average velocity, the final velocity after 12 seconds can be calculated as the average of the average velocities for the first 5 seconds and the next 10 seconds.
- The final velocity after 12 seconds can be found by substituting the values of A, initial velocity, and time into the