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A particle moves on circular path of radius 5m with constant speed 5m/s. Find the magnitude of its average acceleration when it completes half revolution.?
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Calculation of Average Acceleration of a Particle Moving on Circular Path

Given:
Radius of circular path, r = 5m
Speed of particle, v = 5m/s

Formula:
Average acceleration, a_avg = Δv/Δt

Explanation:
The particle moving on circular path undergoes a change in velocity due to the change in direction of motion. This change in velocity is known as centripetal acceleration. The magnitude of centripetal acceleration is given by a_c = v^2/r.

When the particle completes half revolution, it moves from one end of the diameter to the other end, i.e., it changes its direction completely. Therefore, the change in velocity, Δv = 2v. The time taken to complete half revolution, Δt = πr/v.

Calculation:
Substituting the given values in the formula for average acceleration, we get:
a_avg = Δv/Δt
a_avg = 2v/(πr/v)
a_avg = 4v^2/πr^2
a_avg = 4(5^2)/π(5^2)
a_avg = 20/π
a_avg ≈ 6.37 m/s^2

Conclusion:
The magnitude of average acceleration of the particle when it completes half revolution is 6.37 m/s^2.
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A particle moves on circular path of radius 5m with constant speed 5m/s. Find the magnitude of its average acceleration when it completes half revolution.?
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