Kinematics: Velocity and Acceleration – Rankers Physics

Average Speed and Velocity: Practice Problem & Solution

Assertion (A): If velocity of a particle moving in a straight line is zero at a point, its acceleration will be zero at that point. Reason (R): Wherever \(a = v \frac{dv}{dx}\) holds, \(v = 0 \Rightarrow a = 0\).  
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:

Assertion (A) is false. For example, a ball thrown vertically upwards has zero velocity at its highest point, but its acceleration is \(g\).
Reason (R) is false. While the formula \(a = v \frac{dv}{dx}\) is correct, the implication \(v = 0 \Rightarrow a = 0\) from this formula is physically incorrect as \(dv/dx\) itself might be undefined or lead to physically inconsistent conclusions when \(v=0\). Physically, \(a = dv/dt\), which can be non-zero when \(v=0\).

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