As shown in the figure, a particle is moving with constant speed π m / s. Considering its motion from A to B, the magnitude of the average velocity is :

Solution

Physics sir · 3 steps

Average velocity is the straight chord from A to B divided by the time spent on the arc.

1. Time on the arc. Let the radius be R. The angle 120° = 2π/3 rad, so the arc length is (2π R)/3. At speed π m s⁻¹ the time taken is t = (2π R/3)/π = 2R/3.
2. Displacement. Displacement is the chord AB, not the arc. For a central angle θ the chord is 2R sin θ/2 = 2R sin 60° = √3 R.

   |v⃗_(avg)| = (√3 R)/(2R/3) = 3√3/2 = 1.5√3 m s⁻¹

3. So. The radius cancels, and the magnitude of the average velocity is 1.5√3 m s⁻¹, option (b).

The idea to keep. On a circle, average speed uses the arc but average velocity uses the chord 2R sin θ/2. If R is not given, keep it as a symbol; it will cancel.

Answer from the NTA final answer key. Solution by PrepWiser.