Kinematics: Average vs. Instantaneous Velocity – Rankers Physics

Graphs of Motion: Practice Problem & Solution

Assertion (A): For a moving particle on a straight line magnitude of average velocity between any two points will be less than magnitude of instantaneous velocity at every point between them. Reason (R): In \(x-t\) graph slope of chord joining two points gives average velocity between them.  
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 Graphs of Motion. Understanding the underlying formula is key to arriving at the correct answer below:

Assertion (A) is false. The magnitude of average velocity can be equal to or greater than the magnitude of instantaneous velocity at some points, or less than at others. For constant velocity, they are equal.

Reason (R) is true. By definition, the slope of the chord in an \(x-t\) graph represents the average velocity. However, since Assertion (A) is false, option (4) is selected.

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