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Is acceleration noise modelled differently in EKF and UKF Kalman Filters?

In a lecture on basic Kalman filter, I came across the following assumption about acceleration noise.

Acceleration Noise in Normal Kalman Filter

Every component of the noise vector $\nu$ is itself a product of time and acceleration values. Nothing is known about the accelerations $a_x$ and $a_y$ but each component of $\nu$ is assumed to have zero mean and every pair of components $\nu_j$, $\nu_k$ has some known variance $\sigma^2_{\nu_j\nu_k}$. As a consequence the last term in each of the four equations is set to zero (not shown here). The covariance matrix Q contains time though as in the screenshot below. enter image description here

In a latter lecture on Unscented Kalman Filter the assumption was changed as below. enter image description here

Here the components of noise vector $\nu$ do not contain any effect of time. These time-free components are assumed to have mean zero and covariance $Q$. As a result their effect on the mean state vector $x$ cannot be set to zero. Also $Q$ is independent of time.

Is it standard practice to make different kind of assumptions?