Ratio of Average Velocity – Rankers Physics

Average Speed and Velocity: Practice Problem & Solution

A particle starts from rest with constant acceleration. The ratio of average velocity to the time average velocity is: (1999)
\(\frac{1}{2}\)
\(\frac{3}{4}\)
\(\frac{4}{3}\)
\(\frac{3}{2}\)

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:

For constant acceleration starting from rest, the displacement \(S = \frac{1}{2}at^2\). The average velocity over time (t) is \(v_{avg} = \frac{S}{t} = \frac{1}{2}at\). The final velocity at time (t) is (v = at). The question asks for the ratio of average velocity to final velocity (assuming "time average velocity" refers to final velocity). Ratio is \(\frac{(1/2)at}{at} = \frac{1}{2}\).

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