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in our last video we had talked about
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average velocity and average speed in
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our this video we will talk about
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instantaneous velocity and instantaneous
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speed now velocity of particle at any
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instant of time or at any point of its
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path is called instantaneous velocity
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now to explain this consider this point
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p is brought more and more closer to
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p and now we calculate the average
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velocity over such a small displacement
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interval instantaneous velocity can be
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defined as the limiting value of average
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velocity where second Point come closer
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and closer to the first point here
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second point is q and first point is p
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now limiting value so limiting value of
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delta X upon delta T as this delta T
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approaches zero is written as DX upon DT
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and this DX upon DT is derivative of x x
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with respect to T this instantaneous
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velocity is equals to
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as Point Q approaches Point p in this
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limit slope of the cord
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PQ becomes equal to slope of tangent of
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the curve at Point P here in the figure
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you can see that this slope this slope
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gives the instantaneous velocity
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of the particle at this point P thus we
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can say that instantaneous velocity at
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any point of a coordinate time graph is
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equal to the slope of tangent to the
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graph at that point now instantaneous
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speed or speed is the magnitude of the
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Velocity unlike the case of average
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velocity and average speed where average
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speed over a finite interval of time may
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be greater than or equal to average
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velocity a unit of average velocity and
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speed or instantaneous velocity or
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second now after instantaneous velocity
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and speed we will talk about
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acceleration now acceleration is rate of
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change of velocity with time now for
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describing Aver a acceleration we first
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consider the motion of an object along
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xais now suppose that
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time T1 the object is at Point
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velocity V1 and at time T2 particle is
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at Point Q moving with
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V2 so average acceleration of an object
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moving from point P to Q is
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T1 and is equal to Delta V upon delta
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T which is the change in velocity of
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object with the passage of time
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is average is acceleration
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acceleration after average acceleration
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instantaneous acceleration instantaneous
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acceleration can be defined in the same
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way as we have defined instantaneous
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so instantaneous acceleration equal to
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0 Delta V upon delta T which is equals
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DT where DV upon DT is derivative of
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velocity V with respect to time
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t no the instantaneous acceleration at
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any instant is equal to the slope of
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velocity time graph at that instant now
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in this figure instantaneous
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acceleration at Point p is equal to the
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slope of tangent to the graph at this
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P now since velocity of the moving
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object has both magnitude and Direction
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likewise acceleration depending on
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velocity has both magnitude and
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Direction so acceleration like velocity
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quantity acceleration can also be
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zero and SI unit of acceleration is
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m/ second Square so this is all for now
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and in our next video we will discuss
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motion with constant acceleration
