How much force would it take to push a larger friend, who has a mass of [tex]m[/tex], to accelerate at a rate of [tex]4 \, \text{m/s}^2[/tex]?



Answer :

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].