Assertion (A): At any instant, acceleration of a body can change its direction without any change in the direction of velocity.
Reason (R): At any instant, direction of acceleration is same as that of direction of change in velocity vector at that instant.
Solution:
Concept: Relationship between acceleration and velocity.
Formula: \(vec{a} = \frac{d\vec{v}}{dt}\).
Solution: (A) is true. For example, a car moving straight can accelerate forward, then brake (accelerate backward) while its velocity direction remains forward. (R) is true; acceleration is defined as the rate of change of velocity, so its direction is the same as the direction of the change in velocity. (R) correctly explains (A) by providing the fundamental definition.
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