Question

Given the table for x, force in Newtons and y, acceleration in meters per second squared: x - force (Newtons) 10 15 8 12 20 y - acceleration (m/s^2) 2 3 1.6 2.4 4, write an equation to show the relationship between x and y.

Answer 1

To determine the relationship between force (x) and acceleration (y), we can start by examining the provided data points. We first note the pairs of values for x (force in Newtons) and y (acceleration in m/s²):

- (10, 2)
- (15, 3)
- (8, 1.6)
- (12, 2.4)
- (20, 4)

Since force (x) and acceleration (y) are related by Newton's second law of motion, which states that \( F = m \cdot a \), we can express this as:

\[ a = \frac{F}{m} \]

Here, \( a \) is acceleration (y), \( F \) is force (x), and \( m \) is mass. From the given data, we can derive the mass if we assume it is constant.

We can calculate \( m \) using the force and acceleration values for specific data points. For example, using the first data point (10 N and 2 m/s²):

\[ m = \frac{F}{a} = \frac{10 \, \text{N}}{2 \, \text{m/s}^2} = 5 \, \text{kg} \]

We can verify this with other data points:

- For (15 N, 3 m/s²):
\[ m = \frac{15}{3} = 5 \, \text{kg} \]

- For (20 N, 4 m/s²):
\[ m = \frac{20}{4} = 5 \, \text{kg} \]

Since the mass consistently evaluates to 5 kg, we can write our equation relating force and acceleration as follows:

### Final Equation:
\[ y = \frac{x}{5} \]

OR

\[ x = 5y \]

This equation indicates that acceleration y is directly proportional to the force x with a constant factor of \( \frac{1}{5} \).