Rotational kinematic equations:

$\overline{){{\mathbf{\omega}}}_{{\mathbf{f}}}{\mathbf{=}}{{\mathbf{\omega}}}_{{\mathbf{0}}}{\mathbf{}}{\mathbf{+}}{\mathbf{}}{\mathbf{\alpha}}{\mathbf{t}}\phantom{\rule{0ex}{0ex}}{\mathbf{\u2206}}{\mathbf{\theta}}{\mathbf{=}}\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{(}}{{\mathbf{\omega}}}_{{\mathbf{0}}}{\mathbf{+}}{{\mathbf{\omega}}}_{{\mathbf{f}}}{\mathbf{)}}{\mathbf{t}}\phantom{\rule{0ex}{0ex}}{\mathbf{\u2206}}{\mathbf{\theta}}{\mathbf{=}}{{\mathbf{\omega}}}_{{\mathbf{0}}}{\mathbf{t}}{\mathbf{}}{\mathbf{+}}\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{\alpha}}{{\mathbf{t}}}^{{\mathbf{2}}}\phantom{\rule{0ex}{0ex}}{{\mathbf{\omega}}}_{{\mathbf{f}}}^{{\mathbf{2}}}{\mathbf{=}}{{\mathbf{\omega}}}_{{\mathbf{0}}}^{{\mathbf{2}}}{\mathbf{+}}{\mathbf{2}}{\mathbf{\alpha}}{\mathbf{\u2206}}{\mathbf{\theta}}}$

**(a)**

Tangential acceleration:

$\overline{){{\mathbf{a}}}_{{\mathbf{t}}}{\mathbf{=}}{\mathbf{r}}{\mathbf{\alpha}}{\mathbf{=}}{\mathbf{r}}\frac{\mathbf{\u2206}\mathbf{\omega}}{\mathbf{\u2206}\mathbf{t}}}$

During a very quick stop, a car decelerates at 7.00 m/s.

(a) What is the angular acceleration of its 0.280-m-radius tires, they do not slip on the pavement?

(b) How many revolutions do the tires make before coming to rest, given their initial angular velocity at 95.0 rad/s?

(c) How long does the car take to stop completely?

(d) What distance does the car travel in this time?

(e) What was the car's initial velocity?

(f) Do the values obtained seem reasonable, considering that this stop happens very quickly?

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