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When more distance is covered within less interval of time while the object is moving, then it is said that velocity of the object is increasing. For example, when we are travelling from the place A to place B, At first if we cover 3 km in 15 min, and after some time, if we travel at a velocity of 5 km in 15 min, then, it is said that the velocity is increasing
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WHEN there is an external influence called a FORCE on an object, then the force gives acceleration to that object. the acceleration causes increase in the velocity.

If you are on a motorbike, and have started it, but it is stationary there is no force. But if you raise the accelerator, (and change the gear), then the vehicle runs forward with a great push.  That is the force by engine. So the velocity increases from 0 to a finite value.

Velocity = increase in displacement divided by time duration

As the body travels more displacement in the same time duration, its velocity increases.

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