Average acceleration from average velocity?

[Fizz_Geek]

Homework Statement

A particle travels from point A to point B following a semicircular path (a half-circle) of radius 5 m, and it travels at a constant speed of 1 m/s. Find the average acceleration of the particle.

Homework Equations

Average acceleration = change in velocity/ change in time

Total time = distance / speed

The Attempt at a Solution

I already know the answer, and I understand why it's true:

v0 = 1 m/s
vf = -1 m/s

total time = (5 pi m) / (1 m/s) = 5pi seconds

Avg acceleration = (2 / (5pi) ) m/s^2

My question is: Is the average acceleration ever equal to the (average velocity/ time) ? In this case, I know it's not because:

Avg velocity = displacement / time = 10 m / 5pi sec = (2/ pi) m/s

And, if I divided by the time, I would get a factor of pi^2 in the denominator, which is not in my original answer.

I would really appreciate any help sorting this out!

 

[mfb]

Consider a 1-dimensional motion, ##v(t)=v_0 + at## with constant a, from t=0 to T. The average acceleration is a, the average velocity is v₀+aT/2. As you are free to choose v₀, you can get your equality.

Particles at rest have zero average velocity and acceleration, they are a special case of my example for a=0.