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Instantaneous Velocity and Speed

The average velocity tells us how fast an object has been moving over a given time interval but does not tell us how fast it moves at different instants of time during that interval. For this, we define instantaneous velocity or simply velocity V at an instant t.

The velocity at an instant is defined as the limit of the average velocity as the time interval becomes infinitesimally small. In other words,
where the symbol stands for the operation of taking limit as of the quantity on its right. In the language of calculus, the quantity on the right hand side of Eq. (i) is the differential coefficient of x with respect to t and is denoted by . It is the rate of change of position with respect to time, at that instant.

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