Final answer:
The derivatives zs and zt refer to partial derivatives of z with respect to s and t. The derivative zt can be found if z is a function of time, such as in kinematic equations. Without an explicit function relating z to s, zs cannot be determined.
Step-by-step explanation:
To find the derivatives zs and zt, we would first need a functional relationship expressing z as a function of s and t. However, based on the information provided, it appears that the question might be related to physics, particularly kinematics, where z might represent the position of a particle along the z-axis, and t represents time. The formulae given suggest motion equations with initial position xo and initial velocity vo with constant acceleration a.
If there's an explicit function of z (possibly representing displacement) in terms of s and t, the derivatives zs and zt would correspond to the partial derivatives of z with respect to s and t respectively. For zt, if we assume z(t) = zo + vot + ½at2 where zo, vo, and a are constants, then zt, the derivative of z with respect to t, would be dz/dt = vo + at.
Since the relationship between z and s is not specified, we cannot provide the derivative zs without additional information. If s is a variable that affects z, this would need to be defined by a specific equation or context.