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Assertion: The average velocity of the object over an interval of time is either smaller than or equal to the average speed of the object over the same interval.
 Reason: Velocity is a vector quantity and speed is a scalar quantity.  ( )
A. If both assertion and reason are true and the reason is the correct explanation of the assertion.  
B. If both assertion and reason are true but reason is not the correct explanation of the assertion.  
C. If assertion is true but reason is false.  
D. If the assertion and reason both are false

Answer

B
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Solution

\(Average \;speed=\dfrac{Total\;distance}{Total\;time}\)

\(Average \;velocity=\dfrac{Total\;displacement}{Total\;time}\)
We know that displacement is the shortest length between two points and distance is the actual length covered by the body. Displacement is vector quantity and it is the difference between the position vector of two points. Distance is a scalar quantity.
As, displacement \(\leq\) distance hence velocity \(\leq\) speed. 
As displacement is vector quantity, velocity is also vector quantity and as distance is a scalar quantity speed is also scalar quantity.
Therefore, the assertion and reason are true but reason is not the correct explanation of the assertion.  
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