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Physics

Assertion (A) : For a given time interval, average velocity and average speed can have different values.

Reason (R) : Speed is a scalar quantity whereas velocity is a vector quantity.

  1. both A and R are true and R is the correct explanation of A
  2. both A and R are true and R is not the correct explanation of A
  3. assertion is false but reason is true
  4. assertion is true but reason is false

Motion in One Dimension

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Answer

both A and R are true and R is the correct explanation of A

Explanation

Assertion (A) is true because :

average speed=total distancetotal time\text {average speed} = \dfrac {\text {total distance}}{\text {total time}}

and

average velocity=net displacementtotal time\text {average velocity} = \dfrac {\text {net displacement}}{\text {total time}}

So if the path is not straight (e.g., in a circular or zig-zag path), distance > displacement, so average speed > average velocity in such cases.

Reason (R) is true because speed has only magnitude (no direction) i.e., scalar and velocity has both magnitude and direction i.e., vector. Hence, the reason correctly explains why average speed and average velocity can differ because velocity depends on displacement (vector) and speed depends on distance (scalar).

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