Negative acceleration is called retardation or deceleration ( the opposite of accelaration ). If the velocity of a body is decreasing with respect to time, the acceleration is said to be negative. Retardation is the rate of decrease in velocity .
If there was no retardation then no body will ever be able to stop.
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Examples:
1) When apply break to stop a car then also acceleration is -ve
2) Landing of a eroplane
3) When fan is switched off
4) A train reaching at a station to stop
5) stone thrown upwards
6) When a fun ride like roller costers is about to stop
7) deceleration of moving cradle after sometime of applying force
8) When a ball thrown upward then acceleration due to gravity acts downward and taken as -ve