Solve.
-While traveling at a constant speed in a car, the centrifugal acceleration passengers feel while the car is turning varies inversely as the radius of the turn. If the passengers feel an acceleration of 6 feet per second per second
When the radius of the turn is 80 feet, find the acceleration the passengers feel when the radius of the turn is 160
Feet.
A)6 feet per second per second
B)3 feet per second per second
C)4 feet per second per second
D)5 feet per second per second

Question

Quizplus · Accepted Answer

Since the centrifugal acceleration varies inversely as the radius of the turn, we can use the formula $a \propto \frac{1}{r}$, where $a$ is the acceleration and $r$ is the radius of the turn. We can write this as $ar = k$, where $k$ is a constant. If the acceleration is 6 feet per second per second when the radius is 80 feet, then we have $6(80) = k$, so $k = 480$. When the radius is 160 feet, we have $ar = 480$ again, but now $r = 160$, so we can solve for $a$: $a(160) = 480$ $\Rightarrow$ $a = 3$. Therefore, the passengers feel an acceleration of 3 feet per second per second when the radius of the turn is 160 feet. The answer is B. Let a be the acceleration and r be the radius of the turn. Then we know that ar = k for some constant k. When r = 80 and a = 6, we have 80(6) = k, so k = 480. When r = 160, we have a(160) = 480, so a = 3. Therefore, the acceleration the passengers feel when the radius of the turn is 160 feet is 3 feet per second per second. Thus, the answer is B, 3 feet per second per second.

Solve. -While Traveling at a Constant Speed in a Car, the the Centrifugal