Sure, let's work through this step-by-step to determine the required force.
First, recall Newton's second law of motion which states that force is the product of mass and acceleration. The formula is given by:
[tex]\[ F = m \cdot a \][/tex]
where:
- \( F \) is the force,
- \( m \) is the mass of the object,
- \( a \) is the acceleration.
Here are the details provided in the question:
- The mass of the larger friend ( \( m \) ) is 70 kilograms.
- The acceleration ( \( a \) ) is 4 meters per second squared ( \( m/s^2 \) ).
By substituting the given values into the formula, we can calculate the force. So:
[tex]\[ F = 70 \, \text{kg} \cdot 4 \, \text{m/s}^2 \][/tex]
When we multiply these values together:
[tex]\[ F = 280 \, \text{N} \][/tex]
Thus, the force required to push the larger friend, accelerating them at [tex]\( 4 \, \text{m/s}^2 \)[/tex], is [tex]\( 280 \, \text{Newtons} \)[/tex].
