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question 8
if a car goes around a semi - circular corner twice as fast, what happens to the resulting centripetal acceleration?
the centripetal acceleration remains the same
the centripetal acceleration quadruples
the centripetal acceleration doubles
the centripetal acceleration is cut in half

Explanation:

Step1: Recall centripetal - acceleration formula

The formula for centripetal acceleration is $a_c=\frac{v^{2}}{r}$, where $v$ is the velocity and $r$ is the radius of the circular path.

Step2: Analyze the effect of doubling the velocity

Let the initial velocity be $v_1 = v$ and the new velocity be $v_2 = 2v$. The initial centripetal acceleration is $a_{c1}=\frac{v_1^{2}}{r}=\frac{v^{2}}{r}$, and the new centripetal acceleration is $a_{c2}=\frac{v_2^{2}}{r}=\frac{(2v)^{2}}{r}=\frac{4v^{2}}{r}$.

Step3: Compare the initial and new centripetal - accelerations

We can find the ratio $\frac{a_{c2}}{a_{c1}}=\frac{\frac{4v^{2}}{r}}{\frac{v^{2}}{r}} = 4$. So, when the velocity doubles, the centripetal acceleration quadruples.

Answer:

The centripetal acceleration quadruples