A particle moves on circular path of radius 5m with constant speed 5 m/s. The magnitude of its average acceleration when it completes half revolution is :-

The average acceleration of an object moving in a circular path is given by the formula:

a_avg = Δv / Δt

However, in this case, the speed of the particle is constant, which means there is no change in speed (Δv = 0). Therefore, the average acceleration of the particle is 0 m/s².

But if you are referring to the average angular acceleration, it's a different scenario. Angular acceleration is the rate of change of angular velocity. In a half revolution of a circle, the change in velocity direction is pi radians (180 degrees), but the magnitude of the velocity remains the same.

So, even though the speed (magnitude of velocity) is constant, the velocity changes because its direction changes. The average acceleration in this case is not zero because it's the change in velocity (which includes direction, not just speed) divided by the time taken.

The time taken for half a revolution is the distance (half the circumference of the circle) divided by the speed:

t = (1/2) * 2πr / v t = πr / v t = π * 5m / 5 m/s = π seconds

The final velocity v_f is the initial velocity v_i rotated by 180 degrees. The change in velocity Δv is then:

Δv = v_f - v_i Δv = 2v

The magnitude of the average acceleration a_avg is then:

a_avg = Δv / Δt a_avg = 2v / t a_avg = 2 * 5 m/s / π s = 10/π m/s²

So, the magnitude of the average acceleration of the particle when it completes half a revolution is 10/π m/s².