Aiyana drives for 100 s at a rate of 20m/s, then turns around and drives for another 200 s at a rate of 30m/s and completes the rest of her journey at a rate of 90m/s for 100 s. what is her average velocity?
Divide her net distance travelled by 400 seconds.
The answer will depend upon her direction when traveling at 90 m/s. this is not clearly stated.
Displacement = (-20)•100 +30•200+90•100= =13000 m.
Ave velocity = displacement/time taken =
= 13000/400 =32.5 m/s.
To find the average velocity, we need to calculate the total displacement and divide it by the total time taken.
First, let's calculate the displacement for each segment of Aiyana's journey.
In the first segment, Aiyana drives for 100 s at a rate of 20 m/s. Therefore, the displacement in this segment is calculated as:
displacement1 = (rate1) * (time1) = (20 m/s) * (100 s) = 2000 meters
In the second segment, Aiyana drives for 200 s at a rate of 30 m/s. Therefore, the displacement in this segment is calculated as:
displacement2 = (rate2) * (time2) = (30 m/s) * (200 s) = 6000 meters
In the third segment, Aiyana drives for 100 s at a rate of 90 m/s. Therefore, the displacement in this segment is calculated as:
displacement3 = (rate3) * (time3) = (90 m/s) * (100 s) = 9000 meters
Now, let's calculate the total displacement by adding up the displacements from each segment:
total displacement = displacement1 + displacement2 + displacement3 = 2000 + 6000 + 9000 = 17000 meters
Next, we calculate the total time taken for Aiyana's journey:
total time = time1 + time2 + time3 = 100 + 200 + 100 = 400 seconds
Finally, we can calculate the average velocity by dividing the total displacement by the total time:
average velocity = total displacement / total time = 17000 meters / 400 seconds = 42.5 m/s
Therefore, Aiyana's average velocity for the entire journey is 42.5 m/s.