To find the average velocity for the 20 seconds, we can divide the total displacement by the total time taken.
In the first 10 seconds, the body starts from rest and uniformly accelerates until its velocity becomes 100 m/s. We can use the equation of motion:
v = u + at
Where: v = final velocity u = initial velocity (0 m/s, as it starts from rest) a = acceleration t = time
Rearranging the equation, we have:
a = (v - u) / t
Substituting the given values, we have:
a = (100 m/s - 0 m/s) / 10 s a = 10 m/s²
Since the body starts from rest, its initial velocity (u) is 0 m/s. We can calculate the displacement (s) using the equation:
s = ut + (1/2)at²
Substituting the values:
s = 0 + (1/2)(10 m/s²)(10 s)² s = 0 + 500 m s = 500 m
Now, in the next 10 seconds, the body maintains a constant speed of 100 m/s. The displacement during this time will be:
s = v * t s = 100 m/s * 10 s s = 1000 m
The total displacement for the 20 seconds is the sum of the displacements during the two intervals:
Total displacement = 500 m + 1000 m Total displacement = 1500 m
The average velocity is then calculated as the total displacement divided by the total time:
Average velocity = Total displacement / Total time Average velocity = 1500 m / 20 s Average velocity = 75 m/s
Therefore, the average velocity for the 20 seconds is 75 m/s.