How do you calculate the average acceleration of a particle in circular motion?

[brandon26]

A particle moves in a semi circular path AB of radius 5m with constant speed of 11s^-1.

What is its average acceleration:

I worked it out but it was wrong, what i did was:

average acceleration = average velocity / time and got 4.8ms^-2.

Someone help please?

 

[David]

This problem is a little more complex the way I read it. I assume is asking for the average vector acceleration not the average magnitude of the acceleration vector.

So what you have to do is work out what the acceleration is at any point on the semi-circular path (you should know an expression for the radial acceleration of a body moving in a circle.) Then you need to integrate over the path to get the average acceleration. You can do that integral by components, and you can see by symmetry of hte situation that one of the integrals is zero.

So when you figure out the geometry, etc, you'll find that you basically need to work out what one component of the acceleration is along the semi-circular path, and then average it using the integral.

 

[Päällikkö]

Isn't it simply $$a_c = \frac{v^2}{r}$$?
What's a semicircular path?

 

[David]

I interpreted the question to mean that you only consider the average over half a circle and that is why the semicircular path is mentioned and the "average" acceleration is asked for.

 

[Doc Al]

Another way to solve it is to simply use the definition of average (vector) acceleration:
$$\vec{a}_{ave} = \frac{\Delta \vec{v}}{\Delta t}$$