Assertion : An object has been given two velocities $\vec{v_{1}}$ and $\vec{v_{2}}$ , then it has a resultant velocity $\vec{v} = \vec{v_{1}} + \vec{v_{2}}$ .
Reason : $\vec{v_{1}}$ and $\vec{v_{2}}$ should be velocities with reference to some common reference frame.

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Both assertion and reason are true and reason is the correct explanation of assertion.

Both assertion and reason are false.

Both assertion and reason are true but reason is not the correct explanation of assertion.

Assertion is true but reason is false.

answer is B.

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Detailed Solution

The resultant of the two velocities $\vec{v_{1}}$ and $\vec{v_{2}}$ is the vector addition using parallelogram law of vector addition. $\vec{v} = \vec{v_{1}} + \vec{v_{2}}$

Both of the velocities must be from same frame of reference, for example: if a object is given two velocities and if one of the velocity is measured from a moving frame of reference and other from a stationary frame of reference. the addition of these velocities will not give the correct value of velocity of object.

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