No, the change in speed does not necessarily equal zero if an object travels at a speed of v in one direction and then changes its direction to travel at a speed of v in the opposite direction.
When an object changes its direction, even if it maintains the same magnitude of speed (v) in both directions, we still consider it as a change in velocity. Velocity is a vector quantity that includes both speed and direction. So, when an object changes direction, its velocity changes, even though the speed remains the same.
In terms of the change in velocity, we consider the initial and final velocities of the object. If the object initially moves at a velocity of v in one direction and then reverses its direction to move at a velocity of -v, the change in velocity is the difference between the final and initial velocities:
Change in velocity = Final velocity - Initial velocity = (-v) - v = -2v
Therefore, the change in velocity would be -2v, indicating a change in direction and a magnitude of 2v in comparison to the initial velocity. It's important to note that the change in velocity is not zero, even though the magnitude of speed remains the same.