The distance, d, an acceleration rate, in meters per second per second. If a car accelerates from a stop at the rate of 20 meters per second per second and travels a distance of 80 meters, about how many seconds did the car travel?

Options

A. Between 1 and 2
B. Between 2 and 3
C. Between 3 and 4
D. 4

Answer

To solve the problem, we will use the equations of motion to find the time it takes for the car to travel a distance of 80 meters while accelerating from rest at a rate of 20 meters per second squared.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Acceleration (a) = 20 m/s²
- Distance (s) = 80 m
- Initial velocity (u) = 0 m/s (since the car starts from rest)

2. **Use the Second Equation of Motion:**
The second equation of motion is:
\[ s = ut + \frac{1}{2} a t^2 \]
Plugging in the known values:
\[ 80 = 0 \cdot t + \frac{1}{2} \cdot 20 \cdot t^2 \]
This simplifies to:
\[ 80 = 10 t^2 \]

3. **Rearranging the Equation:**
To isolate \( t^2 \), we divide both sides by 10:
\[ t^2 = \frac{80}{10} = 8 \]

4. **Taking the Square Root:**
Now, we take the square root of both sides to find \( t \):
\[ t = \sqrt{8} = 2\sqrt{2} \]

5. **Calculating the Approximate Value of t:**
We can calculate \( 2\sqrt{2} \):
\[ \sqrt{2} \approx 1.414 \implies 2\sqrt{2} \approx 2 \times 1.414 \approx 2.828 \]

6. **Conclusion:**
The time \( t \approx 2.828 \) seconds, which lies between 2 and 3 seconds.

### Final Answer:
The car traveled for approximately between 2 and 3 seconds.