Denominator doubled

Question

Originally $a = 12 \space m/s$, then $r$ is doubled. Find the new value for $a$. $a = v^2/r$. If I am right, $v$ is originally $6$ which then turns to $36$ so if you divide it by $3$ it gives you $12$. Later if you double $r$, it would be $6$ which the final answer would be $6$.

Answer 1

You're right.

Since $a=v^2/r$, $a$ is inversely proportional to $r$.

Doubling $r$ halves $a$, and $6\text{ }m/s^2$ is half of $12\text{ }m/s^2.$

Answer 2

Assuming $v$ stays constant, $$ar = v^2 = k$$ where $k$ is a constant. So $a$ and $r$ are inversely proportional. If $r$ is doubled, $a$ is halved, and the new acceleration is $$\frac12(12\frac{m}{s^2})=6 \frac{m}{s^2}$$