In one second a particle moves with constant speed from point A to point B along the circular track of radius 1.0 m as shown in the figure. The average acceleration of the particle (in m/s 2 ) during

Question

In one second a particle moves with constant speed from point A to point B along the circular track of radius 1.0 m as shown in the figure. The average acceleration of the particle (in m/s $^{2}$ ) during this motion is found to be $n π$ where n is an integer. Find the value of n . [Particle is moving from A to B in clockwise direction.]

TestHub · Accepted Answer

Average acceleration = Δ t Δ v ​ Δ v = v B ​ − v A ​ since speed is constant, its magnitude is v at both points Now v = ω r & ω = constant as v is constant so ω = Δ t Δ θ ​ [Angle travelled between A to B is π rad .] ω = 1 π ​ rad / s [ As Δ t = 1 sec ] Now a avg ​ = Δ t Δ v ​ = Δ t v ( − i ^ ) − v ( i ^ ) ​ = − 1 2 v i ^ ​ ⇒ a avg ​ = 1 2 v ​ ( − i ^ ) [ v = ω r ] ⇒ a arg ​ = 1 2 ω r ​ = 1 2 × π × 1 ​ = 2 π rad / s 2 Thus n = 2 Ans.

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