Understanding Newton's Second Law and Force Units

This question relates to Newton's second law of motion, a fundamental principle in physics that describes the relationship between force, mass, and acceleration. The law states that the force acting on an object is equal to the product of its mass and acceleration.

Applying Newton's Second Law Formula

The formula provided is:

$F = ma$

Where:

• F represents the force applied to the object.
• m represents the mass of the object.
• a represents the acceleration of the object.

Calculating Force and Determining its Unit

We are given the following values:

• Mass ($m$) = $1 \text{ kg}$
• Acceleration ($a$) = $1 \text{ m/s}^2$

Let's substitute these values into the formula:

$F = (1 \text{ kg}) \times (1 \text{ m/s}^2)$

$F = 1 \text{ kg} \cdot \text{m/s}^2$

The result of the calculation is $1 \text{ kg} \cdot \text{m/s}^2$. The question asks for the standard SI unit used to quantify this force. The unit $\text{kg} \cdot \text{m/s}^2$ is the base unit derived from the formula. In the International System of Units (SI), this specific combination of base units is given a special name to honor Sir Isaac Newton.

The SI Unit of Force: Newton

The standard SI unit for force is defined as the force required to accelerate a mass of one kilogram by one meter per second squared. This unit is called the Newton, symbolized by 'N'.

Therefore, based on our calculation:

$1 \text{ kg} \cdot \text{m/s}^2 = 1 \text{ N}$

So, when an object with a mass of $1 \text{ kg}$ experiences an acceleration of $1 \text{ m/s}^2$, the force is $1 \text{ Newton}$.

Evaluating Other Options

Let's look at why the other options are not the correct SI unit for force:

• Watt (W): This is the SI unit of power, which measures the rate at which energy is transferred or converted. It is defined as one joule per second ($1 \text{ J/s}$).
• Joule (J): This is the SI unit of energy or work. Work is done when a force causes displacement, calculated as force multiplied by distance ($W = Fd$).
• Pascal (Pa): This is the SI unit of pressure, defined as force per unit area ($P = F/A$).

Since the question specifically asks for the unit quantifying force derived from Newton's second law ($F=ma$), the correct SI unit is the Newton.

Conclusion on Force Unit

The calculation $F = 1 \text{ kg} \times 1 \text{ m/s}^2$ results in $1 \text{ kg} \cdot \text{m/s}^2$. This unit is defined in the SI system as the Newton. Hence, the standard SI unit used to quantify this force is Newton.