Acceleration is defined as the rate or speed of something. If a car is accelerating at 1m/s then in 10 seconds, it will be going 10m/s. When something is accelerating, it means that it is constantly getting faster or slower as long as the acceleration is not zero.
If I were to drop this ball, its acceleration would be 9.8m/s because that is the acceleration of gravity. So after 2 seconds the ball will be accelerating at 19.6m/s. This ball would continue to get faster and faster.

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