To find the average velocity of the fly, we need to determine the total displacement and the total time taken.
We know that the initial velocity (u) is 8.0 m/s, and the final velocity (v) is 24 m/s. The time interval (t) is 40 s.
The average velocity (????) is given by the formula:
???? = total displacement / total time
To find the total displacement, we need to calculate the distance covered during the acceleration period and the distance covered during the interval when the velocity remains constant.
During the acceleration period: The fly starts with an initial velocity (u) of 8.0 m/s and reaches a final velocity (v) of 24 m/s. The time interval (t) is 40 s.
Using the equation: v = u + at
We can rearrange it to find the acceleration (a):
a = (v - u) / t
a = (24 - 8) / 40 a = 16 / 40 a = 0.4 m/s²
Using the equation: s = ut + (1/2)at²
We can calculate the distance covered during acceleration:
s₁ = (8.0 * 40) + (0.5 * 0.4 * 40²) s₁ = 320 + 0.5 * 0.4 * 1600 s₁ = 320 + 320 s₁ = 640 m
During the constant velocity interval: The fly moves at a constant velocity of 24 m/s for a time interval of 40 s.
Using the equation: s = vt
We can calculate the distance covered during this interval:
s₂ = 24 * 40 s₂ = 960 m
Now, we can find the total displacement by adding the distances covered during acceleration and the interval:
total displacement = s₁ + s₂ total displacement = 640 + 960 total displacement = 1600 m
The total time taken is 2 times the given time interval (40 s) because the fly experiences the same conditions twice (acceleration and constant velocity):
total time = 2 * 40 total time = 80 s
Finally, we can calculate the average velocity:
???? = total displacement / total time ???? = 1600 / 80 ???? = 20 m/s
Therefore, the average velocity of the fly is 20 m/s.