what is the particle's average velocity in the y direction vy between t=0.200s and t=0.300s?

It is the total distance traveled in the y direction between these two times, divided by the difference in times:

(y(t=0.3) - y(t=0.2)) / (0.3-0.2)

To find the particle's average velocity in the y direction, vy, between t=0.200s and t=0.300s, you need to determine the displacement in the y direction and divide it by the time interval.

The formula for average velocity in the y direction is:

vy = Δy / Δt

To find Δy (displacement in the y direction), subtract the initial y-coordinate from the final y-coordinate:

Δy = y_final - y_initial

Once you have calculated Δy, you can divide it by the time interval Δt:

vy = Δy / Δt = (y_final - y_initial) / Δt

So, to find the particle's average velocity in the y direction, you need to know the y-coordinate at both t=0.200s and t=0.300s and the time interval between those two points.