Question

question 1 of 10 a race car has a centripetal acceleration of 18.75 m/s² as it goes around a curve. if the curve is a circle with radius 12 m, what is the speed of the car? a. 9.8 m/s b. 15 m/s c. 17.2 m/s d. 1.6 m/s

Explanation:

Step1: Recall centripetal - acceleration formula

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

Step2: Rearrange the formula for speed

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

Step3: Substitute given values

Given $a_c = 18.75\ m/s^{2}$ and $r = 12\ m$. Substitute these values into the formula: $v=\sqrt{18.75\times12}$. First, calculate $18.75\times12 = 225$. Then, $\sqrt{225}=15\ m/s$.

Answer:

B. 15 m/s