A car has wheels with a 4
inch radius. If each wheel's rate of turn is 6
revolutions per second, how fast is the car moving in units of inches/sec?

To determine how fast the car is moving in inches per second, we can calculate the linear speed of the car based on the wheel's rotational speed and the radius of the wheel.

### Steps:
1. **Determine the circumference of the wheel:**
   The circumference of a circle is given by the formula:
   \[
   C = 2\pi r
   \]
   where \( r \) is the radius of the wheel.

   Given:
   \[
   r = 4 \text{ inches}
   \]
   So, the circumference \( C \) is:
   \[
   C = 2\pi \times 4 = 8\pi \text{ inches}
   \]

2. **Calculate the distance traveled per revolution:**
   Since the wheel travels one full circumference per revolution, the distance the car moves per revolution is \( 8\pi \) inches.

3. **Determine the speed of the car:**
   The wheel is turning at 6 revolutions per second, so the car's speed \( v \) is:
   \[
   v = \text{(distance per revolution)} \times \text{(revolutions per second)}
   \]
   Substituting the values:
   \[
   v = 8\pi \times 6 = 48\pi \text{ inches per second}
   \]

   Thus, the car is moving at \( 48\pi \) inches per second.

### Final Answer:
The car is moving at approximately \( 48\pi \) inches per second, which is about 150.8 inches per second.

Would you like further details on any of these steps?

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Here are five related questions to expand your understanding:
1. What is the car's speed in feet per second?
2. How would the speed change if the radius of the wheels were doubled?
3. How far would the car travel in 10 seconds at this speed?
4. What is the car's speed in miles per hour (mph)?
5. How many revolutions would the wheel make in 1 minute?

**Tip:** Always remember that the linear speed of an object can be found by multiplying the rotational speed by the circumference of the rotating object!

Learn how to calculate the speed of a car based on the rotational speed of its wheels and the wheel's radius. This problem involves determining the linear speed using the circumference formula and the concept of rotational motion. Suitable for high school students studying geometry and circular motion.

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