Acceleration is generally defined as the time rate of change of velocity. When can it be defined as the time rate of change of speed?

When the velocity doesn't change its direction

Explanation:

Since velocity vector has 2 components: direction and magnitude, and speed is the velocity's magnitude. So if the velocity doesn't change its direction, we essentially use its magnitude, aka speed, to calculate the rate of change for acceleration.

When direction does not change or is not involved/required.

Explanation:

Acceleration is the time rate of change in velocity. This is because like velocity, acceleration is a vector quantity and has to do with change in direction. But then, a particle can still accelerate without a change in direction. In this case, acceleration can be defined as the time rate of change of speed. This is because, since direction is not involved, speed which is a scalar quantity, has nothing to do with direction.

In essence, speed and velocity are the same when direction is not involved or when direction is not changing. Therefore, in the definition of acceleration, if there are no regards for direction, speed can be used in place of velocity.