Assertion (A): In any curved motion magnitude of dot product of unit acceleration vector & unit velocity vector \(|\hat{a} \cdot \hat{v}|\) cannot be equal to 1.
Reason (R): In all accelerated straight line motion \(|\hat{a} \cdot \hat{v}|\) cannot be less than 1.
Solution:
The magnitude of the dot product \(|\hat{a} \cdot \hat{v}| = |\cos\theta|\), where \(theta\) is the angle between \(vec{a}\) and \(vec{v}\). For curved motion, \(vec{a}\) and \(vec{v}\) are never parallel or anti-parallel (\(theta \ne 0^\circ, 180^\circ\)), so \(|\cos\theta| \ne 1\). Thus (A) is true. For straight line motion, \(vec{a}\) and \(vec{v}\) are always parallel or anti-parallel, so \(|\cos\theta| = 1\). Thus (R) is true and implies it cannot be less than 1, and (R) explains (A).
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