Final answer:
A particle changes direction when its velocity crosses zero. At t = 5 s, the velocity is -25 m/s, indicating the particle has reversed direction since t = 3 s. The exact time of the change can be found by setting v(t) = 0 and solving for t, and only considering positive values of time.
Step-by-step explanation:
The particle changes direction when its velocity changes from positive to negative or vice versa. This can be observed when the velocity, given as a function of time v(t), crosses zero. Based on the given information, we know the velocity at t = 5 s is -25 m/s and the acceleration is increasingly negative, which means the particle was slowing down before t = 3 s and started to move in the opposite direction between t = 3 s and t = 5 s. Since the velocity decreases to zero and then becomes negative, the particle changes direction at the point where the velocity is zero.
To find the exact time when the velocity is zero, we would typically set the velocity function to zero and solve for t. Unfortunately, the full functional form of the velocity is not provided in the question. However, if we had the function, and it yielded two solutions, similarly to other examples given, we would discard the negative value since that represents a time before the motion began. Hence, the time when the particle changes direction is the positive value t where the velocity function v(t) = 0.