For no apparent reason, a poodle is running at a constant speed of 5.80 m/s in a circle with radius 2.3 m.

For t_delta = 0.5 s calculate the magnitude of the average acceleration a_av.

I have no idea how to start this problem because I'm trying to use this equation:

a_av = v^2/R

But the answer isn't correct.

I'm always trying to use the equation a_av = (vf - vi)/(t2 - t1)

But I'm not sure how to find vf and vi to subtract the two vectors.

But is centripetal acceleration the same as average acceleration?

What's the point of the problem giving information about time if it's not even used in the process?

Now if you wanted to approximate that in x y coordinates you could do the following:

w = angular frequency = 2pi/period
period = 2 pi r/v
so w = v/r = 5.8/2.3 = 2.52 radians/second
Vx = -5.8 sin wt = 0 at t = 0
Vy = 5.8 cos w t = 5.8 at t = 0
for going in a circle starting at (5.8 , 0)
after .5 s
Vx = 5.8sin1.26radians = -5.52
Vy = 5.8cos1.26 = 1.77

change in Vx = -5.52
change in Vy = 1.77 - 5.8 = -4.03
for acceleration A divide by .5 sec
Ax = -11.04
Ay = -8.06
magnitude of A = sqrt(121+64) = 13.6 etc
but what a waste of time :)

To find the magnitude of the average acceleration (a_av) of the poodle running in a circle, you cannot simply use the equation a_av = v^2/R. This equation is specifically for the centripetal acceleration in circular motion. However, you can use the equation a_av = (vf - vi)/(t2 - t1), as you mentioned.

To find the final velocity (vf) and initial velocity (vi), you need to understand the motion of the poodle in a circle. Since the poodle is running at a constant speed, it means that its magnitude of velocity remains the same throughout the motion. However, the velocity vector keeps changing its direction as the poodle goes around the circle.

To calculate vf and vi, you can consider the poodle's displacement during the time interval t_delta. Since the poodle is moving in a circle, its displacement will be equal to the circumference of the circle. Therefore, you can use the equation s = 2πR to find the displacement.

Given that the radius (R) of the circle is 2.3 m, you can calculate the displacement (s) using s = 2π(2.3). Once you have the displacement, divide it by the time interval t_delta to find the average velocity (v_av) of the poodle during that time interval.

Now, you can assume that the poodle starts at some point in the circle, and after t_delta seconds, it completes a fraction of the circle. The fraction of the circle completed in t_delta seconds is calculated by dividing the angle covered (θ) by the total angle of a circle (2π radians). The angle θ can be calculated using the equation θ = (v_av * t_delta) / R.

To find vf and vi, you can use the equations:

vf = v_av (which is the magnitude of the average velocity)
vi = -v_av (since the velocity vectors at the beginning and end of the time interval are in opposite directions)

Substituting the values of vf and vi into the equation a_av = (vf - vi)/(t2 - t1), along with the values of t_delta and R, will give you the magnitude of the average acceleration (a_av).

Remember to convert the angles to radians if necessary, as most trigonometric functions work with radians.

I hope this explanation helps you understand how to approach and solve the problem.

I suspect the 1/2 second and average was just given to confuse you but you could do it the way I did calculating the change in velocity over he half second and dividing by the time. I suspect that they did not expect you to do all that.

The point is that although the centripetal acceleration is constant, you can approximate it by using
average Acceleration = change in velocity / change in time

By the way that averaging came out a lot closer to the real answer than I thought it would. After all we went almost 1/4 of the way around the circle during that half second.

Oh okay. I think this makes sense. Thanks for the explanation!

For the first Vx, how come the 5.8 is negative?

Okay I understand the problem now and I got the answer right doing it your way.

Thanks a lot for the explanation. It really helped!

I had a question actually... why is your Vx related to the sin? and your Vy related to the cos? isn't it usually the other way around?

The centripetal acceleration is constant:

v^2/r = 5.80^2/2.3 = 14.6 m/s^2