Final answer:
The velocity of a particle is subject to change depending on the acceleration and initial conditions. To find the time when the velocity is 25m/s, one would need the velocity-time function or would derive it through calculus from the given acceleration.
Step-by-step explanation:
The question pertains to the velocity of a particle at a given time, which is a concept in Physics dealing with kinetics and dynamics. From the given information, we can see that the velocity of the particle is changing with time and that there is also a varying acceleration acting on the particle.
The velocity equation (mentioned as 'Equation 3.15' but not provided in the details) and given acceleration values like 9.8 m/s² (which is the acceleration due to gravity) are crucial for solving this problem.
To determine at what time a particle has a certain velocity, one would typically have the velocity-time function or be able to derive it using calculus with the given acceleration function.
The exact time when the particle reaches 25 m/s depends on the initial conditions and the acceleration function provided, which would allow one to integrate the acceleration to find the velocity as a function of time.