Given Data:
- Distance covered in the first 2 seconds (t1) = 20 m
- Distance covered in the next 4 seconds (t2) = 160 m

Step 1: Calculate the Average Velocity for the First 2 Seconds
To calculate the average velocity for the first 2 seconds, we need to use the formula:
Average Velocity = Total Distance / Total Time

In this case, the total distance covered in the first 2 seconds is 20 m, and the total time is 2 s.
So, the average velocity for the first 2 seconds is:
Average Velocity (t1) = 20 m / 2 s = 10 m/s

Step 2: Calculate the Average Velocity for the Next 4 Seconds
To calculate the average velocity for the next 4 seconds, we use the same formula as above but with the given distance and time values.
The total distance covered in the next 4 seconds is 160 m, and the total time is 4 s.
So, the average velocity for the next 4 seconds is:
Average Velocity (t2) = 160 m / 4 s = 40 m/s

Step 3: Calculate the Total Distance Covered in 7 Seconds
To find the total distance covered in 7 seconds, we add the distances covered in the first 2 seconds and the next 4 seconds.
Total Distance (t1 + t2) = Distance (t1) + Distance (t2) = 20 m + 160 m = 180 m

Step 4: Calculate the Average Velocity for 7 Seconds
To calculate the average velocity for 7 seconds, we divide the total distance by the total time.
The total distance covered in 7 seconds is 180 m, and the total time is 7 s.
So, the average velocity for 7 seconds is:
Average Velocity (t1 + t2) = 180 m / 7 s ≈ 25.71 m/s

Step 5: Determine the Final Velocity after 7 Seconds
The final velocity after 7 seconds is the instantaneous velocity at that time.
To find the instantaneous velocity, we need to consider the acceleration of the object.
Since the object starts from rest, we can assume it has a constant acceleration.

Step 6: Calculate the Acceleration
We can calculate the acceleration using the formula:
Acceleration = Change in Velocity / Time

In this case, the change in velocity is the average velocity for the next 4 seconds (t2) minus the average velocity for the first 2 seconds (t1), and the time is 4 s - 2 s = 2 s.
So, the acceleration is:
Acceleration = (Average Velocity (t2) - Average Velocity (t1)) / (t2 - t1)
Acceleration = (40 m/s - 10 m/s) / 2 s = 30 m/s²

Step 7: Calculate the Final Velocity
To calculate the final velocity, we can use the formula:
Final Velocity = Initial Velocity + (Acceleration * Time)

Since the object starts from rest, the initial velocity is 0 m/s, and the time is 7 s.
So, the final velocity after 7 seconds

Given: Initial velocity = u =0m/s Distance travelled =S=20m time =t=2sec. From second equation of motion: S=ut + 1/2 at² 20= 0*2+ 1/2a2² 20=2a a=10m/s² velocity at the end of 2sec: V=u+at =0+10*2 V=20m/s After 4sec, it covers a distance of 160m so, 160=20*4+1/2(a¹)4² 160=80+2a 8a¹=80 a¹=10m/s² It shows acceleration is uniform. So, velocity at end of 7 sec from start: V=u+at = 0 + 10*7 =70m/s ∴the velocity after 7 sec from the start is 70m/s