Give examples to distinguish:
$(i)$ Distance and displacement.
$(ii)$ Speed and velocity.
$(iii)$ Acceleration and retardation.

(N/A) $(i)$ Distance is the total path length covered by an object,while displacement is the shortest distance between the initial and final positions. For example,if a car travels $100 \, m$ along a winding road,the distance is $100 \, m$. However,if the straight-line distance from the start to the end point is $60 \, m$ towards the north,the displacement is $60 \, m$ north.
$(ii)$ Speed is the rate of change of distance,while velocity is the rate of change of displacement. For example,if a body moves in a circular path and returns to its starting point,its displacement is $0$,making its average velocity $0$. However,the total distance covered is not $0$,so the average speed is not $0$.
$(iii)$ Acceleration is the rate of increase of velocity with time,whereas retardation (or deceleration) is the rate of decrease of velocity with time. For example,when a car speeds up to overtake another vehicle,it is accelerating. When the driver applies brakes to stop the car at a traffic signal,the car is undergoing retardation.