Uniform Circular Motion Question (Mechanics/Physics I)

[adamwest]

Uniform Circular Motion Question Please Help! (Mechanics/Physics I)

A car initially traveling eastward turns north by traveling in a circular path at uniform speed as in Figure P6.10. The length of the arc ABC is 200 m, and the car completes the turn in 34.0 s.

(figure attached as "visual.gif")

Figure P6.10
(a) What is the acceleration when the car is at B located at an angle of 35.0°? Express your answer in terms of the unit vectors i and j.
(b) Determine the car's average speed.
(c) Determine its average acceleration during the 34.0 s and express your answer in terms of the unit vectors i and j.

I have properly solved Parts A and B. It is only Part C that I am having trouble with.

Relevant equation is probably just a avg = Δv/Δt

The Attempt at a Solution

Part A: -.2224i m/s^2 + .1558j m/s^2(This is correct)
Part B: 5.88 m/s (This is correct)

Part C: I have tried the following:

a avg = Δv/Δt, and Δv = ((5.88)^2 + (5.88)^2)^1/2 = 8.3189 m/s ==> a avg = (8.3189/34.0 s) = .2447 m/s^2 (not correct)

and

a avg = Δv/Δt, and Δv=(r/t) since it is circular motion and over 34 seconds the change in both x and y are equal to the radius. So Δv= (127.3240 m / 34.0 s) = 3.7448 m/s ==> a avg = Δv/Δt, so a avg = (3.7448 m/s / 34.0 s) = .1101 m/s^2 for both i and j (not correct).

I know I am overlooking something really simple here. I also realize that the signs will be different for i and j, just as they were in part A. Please help! :)

 

[rude man]

Express a_x and a_y accelerations in terms of polar coordinates R and θ.

Then, average x accel = a_x = ∫a_xdt/∫dt
and same for average y accel a_y.

Then avg accel = a = a_x i + a_y j.

 

[haruspex]

a avg = Δv/Δt, and Δv = ((5.88)^2 + (5.88)^2)^1/2

As rude man points out, the acceleration should be a vector. Your a avg = Δv/Δt is correct, but Δv is a vector.

Δv=(r/t) since it is circular motion and over 34 seconds the change in both x and y are equal to the radius.

Good observation, but think about the x and y components of Δv. I.e. the change in v_x and the change in v_y.