Acceleration and Velocity Direction – Rankers Physics

Average Speed and Velocity: Practice Problem & Solution

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.  
Both (A) & (R) are true and the (R) is the correct explanation of the (A)
Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
(A) is true but (R) is false
Both (A) and (R) are false

Solution Explained:

To solve this problem, we apply the core principles of Average Speed and Velocity. Understanding the underlying formula is key to arriving at the correct answer below:

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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