For no apparent reason, a poodle is running counter-clockwise at a constant spee

Question

For no apparent reason, a poodle is running counter-clockwise at a constant speed of 6.00 m/s in a circle with radius 2.2 m . Let v 1 be the velocity vector at time t1, and let v 2 be the velocity vector at time t2. Consider v =v 2v 1 and t=t2t1. Recall that a av=v /t.

Hint: It may be helpful to assume that at time t1, the poodle is on the x-axis, i.e., that the velocity vector v¯1 points along the y-axis.

Part A: For t = 0.6 s calculate the magnitude (to four significant figures) of the average acceleration a av.

Part B: For t = 0.6 s calculate the direction (relative to v 1) of the average acceleration a av

Part C: For t = 8×102 s calculate the magnitude (to four significant figures) of the average acceleration a av.

Part D: For t = 8×102 s calculate the direction (relative to v 1) of the average acceleration a av.

Explanation / Answer

geometry if a = 0 at t = 0
angle from x axis (call it a) = v t/r

Vx = -v sin a
Vy = v cos a

at start a = 0 so
V1x = 0
V1y = v
at time t
V2x = -v sin(vt/r)
V2y = v cos(vt/r)

call change d

d Vx = -v sin(vt/r)
d Vy = v[cos(vt/r)-1]

ax = -(v/t) sin(vt/r)
ay = (v/t)[cos(vt/r)-1]

A) and B) so for our numbers
v/t = 6.0/0.6 = 10
vt/r = 1.636
ax = -10sin(1.636) = - 9.98
ay= 10*[cos(1.636)-1] = - 10.65
|A| =SQRT(ax^2+ay^2) = 14.6 m/s^2
Angle = 46.86 degree

C) and D) v/t = 6.0/0.08 = 75
vt/r = 0.218
ax = -75sin(0.218) = - 16.22
ay= 75*[cos(0.218)-1] = - 1.76
|A| =SQRT(ax^2+ay^2) = 16.32m/s^2

Angle = 6.19 degree

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