The correct answer is Length, mass, and time. These three quantities are considered fundamental in mechanics because all other mechanical quantities can be derived from them. Let's explore why:

• Length (L): Represents distance and is essential for describing position, displacement, velocity, and acceleration.
• Mass (M): Represents the amount of matter in an object and is crucial for understanding inertia, momentum, and force.
• Time (T): Represents the duration of events and is necessary for defining velocity, acceleration, and rates of change.

For instance:

• Velocity is derived as length per unit time (L/T).
• Acceleration is derived as length per unit time squared (L/T²).
• Force is derived as mass times acceleration (M*L/T²).
• Energy (kinetic energy) is derived as one-half times mass times velocity squared (1/2 * M * (L/T)²).

Other options are incorrect because they either include derived quantities (like force, speed, or energy) or omit a fundamental quantity. Therefore, length, mass, and time form the foundation for expressing all mechanical quantities.