The distance travelled by a particle cannot be zero when displacement is not zero because unlike distance which is a scalar, displacement is a vector quantity implying that it has both direction and magnitude.
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If the distance is measured from a point other than the initial position of the object.
The average velocity in a particular direction = distance travelled in that direction / time taken. Velocity is a vector so the direction is important. If I go from A to B and then return to A my average velocity will be zero. My speed, on the other hand, will not be zero.
When the object, whose location is being measured, is at the reference point for measuring displacement.
The amplitude.
The distance from zero on a number line is called the absolute value.