Final answer:
The provided differential equation dz/dt = x + 2 indicates the velocity of a particle along the x-axis but cannot be solved for the time taken to traverse 23 units without the position function x(t) or an initial condition for integration.
Step-by-step explanation:
The question given is related to the kinematics of a particle moving along the x-axis. The given differential equation dz/dt = x + 2 describes the rate of change of position (velocity) of the particle with respect to time, where 'z' is the position along the x-axis and 't' is time. To find the time taken by the particle to traverse a distance of 23 units, one would integrate the velocity function with respect to time and solve for the time 't' that corresponds to a position change of 23 units from the origin.
To answer the initial query, we cannot directly compute the time taken to traverse 23 units without the full functional relationship between z and t. We would need to know the relationship of x with time to integrate it properly or a given initial condition to solve for the constants after integration. As the full position function x(t) is not provided, we are unable to complete the solution with the provided information.