Final answer:
A kg·m²/s² is a unit of work, equivalently known as a joule (J). This is because the formulas for work and kinetic energy both involve the product of the unit of force (newtons) and distance (meters), which translates to kg·m²/s².
Step-by-step explanation:
Option 1 is true: a kg·m²/s² is indeed a unit of work, also known as a joule (J). The gravitational potential energy equation helps explain why joules are equivalent to kilograms multiplied by meters squared per second squared (kg·m²/s²). This is because work and energy have the same units, which are the units of force times distance.
In SI units, work and energy are measured in newton-meters, and given the special name joule (J), where 1 J equals 1 kg·m²/s². The relationship F = ma (Newton's Second Law) indicates that force (F) is mass (kg) times acceleration (m/s²), and therefore, when multiplied by distance (m), gives the units of energy (J). This equivalency is also observed in the units of kinetic energy, which, as a form of energy, can be expressed using the same units.