Velocities and Acceleration on a rolling wheel

[Ignitia]

I have to be missing something very obvious in this.

Homework Statement

A car travels 80km/h on a level road in the positive direction of an x axis. Each tire has a diameter of 66 cm. Relative to a person riding in the car, what is the velocity of a) center, b)top, and c) bottom of the tire? What are the accelerations of the d) center, e)top, and f) bottom of the tire? Relative to a hitchhiker sitting next to the road, what is the velocity of g) center, h)top, and i) bottom of the tire? What are the accelerations of the j) center, k)top, and l) bottom of the tire?

Homework Equations

80km/h = 22.2m/s
r = 33cm = .33m

a = v²/r

For rolling motions
Vtop =2*Vcom (since V from rotation plus V from translation of the rolling wheel makes 2V)
Vbot = 0 (since V from rotation cancels out V from translation of the rolling wheel)

The Attempt at a Solution

a: 0m/s
b: 22.2m/s
c: -22.2m/s
These are correct.

d: a = v²/r = 0²/.33 = 0m/s²
e: a = v²/r = 22.2²/.33 = 1500m/s²
f: a = v²/r = -22.2²/.33 = -1500m/s²
These are correct.

The second part is what is throwing me off.
g: 22.2m/s (moving same velocity as car, so correct)
h: Vtop =2*Vcom = 2*22.2m/s = 44.4m/s (correct)
i: Vbot = 0 (correct)

j: a = 0m/s² (car, hence wheel center, moving at constant velocity, no acceleration. Correct.)
k: ?
l: ?

The answers are 1500m/s² and -1500m/s² respectively. Can someone please explain how?

 

[kuruman]

The velocity of a point on the tire is the vector sum of the velocity of the center of the wheel (an unchanging constant) and the velocity about the center. So both the person in the car and the hitchhiker see that velocity change in exactly the same way. Remember that acceleration is the change in velocity.

 

[Ignitia]

Alright, got it now. Thank you!