Motion transducers — what can be measured directly: Displacement, velocity, and acceleration are all measurable using appropriate motion transducers (e.g., LVDT, tachogenerator/encoder, and accelerometer) designed for each quantity. Evaluate this statement.

Introduction / Context:
Control systems and instrumentation frequently require measurement of position (displacement), speed (velocity), and acceleration. Different transducer families are optimized for each quantity. This question verifies whether all three can be directly measured with suitable sensors rather than always inferring one from another via differentiation or integration in software.

Given Data / Assumptions:

• LVDT and linear encoders for displacement.
• Tachogenerators and incremental/absolute encoders for velocity (direct or derived at high fidelity).
• Accelerometers (piezoelectric, piezoresistive, or MEMS capacitive) for acceleration.

Concept / Approach:
Each motion variable can be sensed by a device whose physical response is proportional to that variable: displacement sensors output proportional change with position; tachogenerators produce voltage proportional to rotational speed; accelerometers produce output proportional to mass * acceleration via inertial effects (e.g., piezoelectric charge, capacitive plate deflection). Although digital systems often compute velocity by differentiating position (or compute displacement by integrating acceleration), dedicated transducers exist to measure each quantity directly with high bandwidth and dynamic range when selected correctly.

Step-by-Step Solution:

Verification / Alternative check:
Industrial drives commonly use encoders for position and speed feedback; vibration monitoring uses accelerometers; structural testing uses LVDTs for displacement. These are standard, off-the-shelf solutions, confirming practical measurability.

Why Other Options Are Wrong:

• Incorrect: Conflicts with widespread industrial practice.
• “Applies only to displacement…”: Acceleration and velocity sensors are ubiquitous (accelerometers, tachos/encoders).
• “Valid only for optical…”: Electromechanical and piezoelectric sensors are very common.
• “Depends solely on sampling frequency”: Sensor physics and dynamic range matter beyond sampling.

Common Pitfalls:
Assuming software differentiation/integration is mandatory; overlooking direct-sensing devices that reduce noise accumulation and simplify control loops.

Final Answer:
Correct.