Carlos and Katherine are estimating acceleration by rolling a ball from rest down a ramp. At 1 second, the ball is moving at 5 meters per second m/s, at 2 seconds, the ball is moving at 10 m/s, at 3 seconds, the ball is moving at 15m/s, and at 4 seconds, it is moving at 20m/s. When graphed on an xy-plane, which equation best describes the ball's estimated acceleration where y expresses speed and x ecpresses time?

Options

A. y=5x+5
B. y=25x
C. y=5x
D. `y=(4x+1)^2+5`

Answer

To solve the problem of estimating the acceleration of the ball based on the given data, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Variables**:
- Let \( x \) represent time in seconds.
- Let \( y \) represent speed in meters per second (m/s).

2. **Record the Given Data**:
- At \( x = 1 \) second, \( y = 5 \) m/s.
- At \( x = 2 \) seconds, \( y = 10 \) m/s.
- At \( x = 3 \) seconds, \( y = 15 \) m/s.
- At \( x = 4 \) seconds, \( y = 20 \) m/s.

3. **Look for a Pattern**:
- From the data, we can observe:
- When \( x = 1 \), \( y = 5 \times 1 = 5 \).
- When \( x = 2 \), \( y = 5 \times 2 = 10 \).
- When \( x = 3 \), \( y = 5 \times 3 = 15 \).
- When \( x = 4 \), \( y = 5 \times 4 = 20 \).

4. **Formulate the Equation**:
- From the observations, we can see that the relationship between \( y \) and \( x \) can be expressed as:
\[ y = 5x \]

5. **Conclusion**:
- The equation \( y = 5x \) describes the ball's estimated acceleration, where \( y \) is the speed and \( x \) is the time.

### Final Answer:
The equation that best describes the ball's estimated acceleration is:
\[ y = 5x \]