a bicycle tire has a radius of 0.23 m. the tire spins at a constant speed with a centripetal acceleration of…

Explanation:

Step1: Recall centripetal - acceleration formula

The centripetal - acceleration formula is $a_c=\frac{v^2}{r}$, where $a_c$ is the centripetal acceleration, $v$ is the tangential speed, and $r$ is the radius.

Step2: Rearrange the formula for tangential speed

We can rewrite the formula $a_c = \frac{v^2}{r}$ to solve for $v$. Multiply both sides of the equation by $r$: $a_cr=v^2$. Then take the square - root of both sides: $v = \sqrt{a_cr}$.

Step3: Substitute the given values

We are given that $a_c = 42\ m/s^2$ and $r = 0.23\ m$. Substitute these values into the formula: $v=\sqrt{42\times0.23}$. First, calculate $42\times0.23 = 9.66$. Then, $v=\sqrt{9.66}\approx3.1\ m/s$.

Answer:

3.1 m/s