# During Instantaneous Velocity The Delta 't' Tends To Zero ?What Does That Mean? plz explain me through an example

lim means in the limit of. Or in other words, it means in the limit that delta T goes to 0. To get instantaneous velocity its important to take the smallest possible amount of time (delta T), but obviously it cannot be 0. So the limit means the value which v tends to as the amount of time tends to 0. (Obviously delta S will also get smaller as you decrease delta T).

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Mathematically instantaneous velocity of an object is the limiting value  of average velocity as $Delta t$ tends towards 0.

Or:

Instantaneous velocity =$displaystylelim_{Delta tto 0}frac{Delta x}{Delta t}$

And instantaneous velocity is also the derivative of the “position of the object” ( “x” ) with respect to “time interval”( “t” )

or, Instantaneous velocity =$frac{d}{d t} x$

In a graph of motion of an object drawn “x” versus “t”; Instantaneous velocity of the object is the slope of tangent line drawn at the position representing that instant.

Instantaneous velocity is a vector quantity and thus have  it’s direction ( positive or negative ) associated with it along with it’s magnitude.

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